Digital quantitative analysis of biomechanical factors of proximal contact loss of first molar implant crown

Abstract

Background

The anterior component of force (ACF) is key to proximal contact loss (PCL) after implant restoration, yet its quantitative impact remains unclear. This study employed digital model analysis to indirectly assess the effects of ACF and examine its association with PCL.

Methods

Following final restoration, 3D surface and buccal occlusal data were obtained from ninety first molar implant sites and mesial adjacent teeth. Occlusal force-induced changes in proximal contact gap (Δd_P) and centroid position (Δd_C) were measured using Geomagic Wrap 2021 for indirect ACF estimation. Proximal contact gaps were measured under non‑occluding conditions at baseline and 6 months to calculate the change over time (ΔD). Univariate and multivariate analyses identified PCL-related biomechanical influencing factors, and a restricted cubic spline (RCS) model was developed and validated using Cohen’s Kappa.

Results

The 6-month PCL incidence was 17.78%, and Δd_P emerged as a significant biomechanical influencing factor of ΔD (P < 0.001). RCS analysis revealed that the adjacent state remains stable when Δd_P is within the range of − 13 μm to 9 μm; beyond this range, imbalance occurs. The model demonstrated good fitting capability (κ = 0.59, P = 0.003).

Conclusion

This study achieved an indirect assessment and quantification of the effect of ACF through digital model analysis technology, and clarified its correlation with the PCL of the implant, providing new evidence and methodological references for related biomechanical research.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s12903-026-08773-x.

Introduction

Proximal contact loss (PCL) is a common complication following implant restoration [1] (Fig. 1A), which can lead to food impaction and patient discomfort, and may even contribute to peri-implantitis, thereby jeopardizing the long-term stability of the restoration [2, 3]. PCL frequently occurs in the mesial contact area of posterior dental implants, yet its precise etiology remains unclear [4–7]. A predominant hypothesis attributes PCL to a biomechanical mismatch: natural teeth, with their periodontal ligaments, possess physiological mobility (manifesting as mesial drift), whereas osseointegrated dental implants remain statically fixed within the alveolar bone [8, 9].

Fig. 1.

Research progress on PCL in dental implants. A, Definition of PCL: In implant-supported restorations, the proximal contact gap is initially tight immediately after prosthesis delivery. Over time, the proximal contact gap gradually widens; when dental floss or a 50-µm thickness gauge passes through the proximal contact area without resistance, PCL is considered to have occurred. B, Schematic illustration of the anterior–posterior component of occlusal force: When ACF exceeds the PCF, adjacent teeth undergo mesial displacement under functional loading, resulting in increased proximal contact gap during occlusion; conversely, when ACF is less than PCF, distal displacement occurs, leading to reduced proximal contact gap. C, Schematic illustration of animal experiments: Natural teeth with varying cusp heights exhibit different rates of mesial migration. The green arrow indicates the movement speed of the natural teeth. D, Schematic illustration of the ACF measurement device: The device quantifies changes in frictional force as a metal strip passes through the proximal contact area before and after occlusion. The blue cubic element functions as an occlusal simulator, transmitting occlusal force while maintaining a defined spatial clearance for sensor integration. E, Schematic illustration of FEA. F, Schematic illustration of the digital measurement method: This approach measures pre- and post-occlusal changes in centroid position and proximal contact gap. The black dots indicate the centroid; the blue lines delineate the proximal contact area boundaries

In fact, the role of occlusal force as a primary intraoral biomechanical factor in PCL remains controversial. The debate specifically centers on whether and to what extent the magnitude, direction, and distribution of functional occlusal forces—particularly their horizontal components— directly drive physiological tooth movement and subsequent loss of proximal contact. While some studies suggest that increased or off-axis occlusal loading may elevate the risk of PCL [10–13], others have found no clear association [6, 7, 14–16], likely due to variations in study design, force measurement methodologies, and sample heterogeneity.

Within this controversy, the anterior component of force (ACF) emerges as a critical yet insufficiently quantified variable [9, 17] (Fig. 1B). Therefore, a precise understanding of ACF, the specific force implicated in physiological mesial drift, is fundamental to clarifying the role of occlusal mechanics in PCL.

Specifically, ACF is a horizontal vector generated along cuspal inclines during jaw closure, with a magnitude that can reach up to five times that of the Posterior component of force (PCF) [18]. However, directly measuring ACF in vivo is exceptionally challenging because its expression is highly variable, influenced by factors such as individual cusp anatomy and specific occlusal contact patterns. Early foundational work, including animal studies, established a link between cusp height variation and differential rates of mesial drift, suggesting the critical role of horizontal forces [19] (Fig. 1C). Subsequent efforts sought to confirm ACF as the principal driver of tooth migration by measuring pressure or friction changes at proximal contacts [18, 20, 21]. While informative, these techniques often involve specialized equipment that complicates their application under realistic, dynamic intraoral conditions (Fig. 1D). In response to these limitations, computational approaches like finite element analysis (FEA) have been employed to model the biomechanics (Fig. 1E). For instance, a study by Qian et al. used 3D FEA to analyze occlusal force direction effects on PCL in anterior implant restorations [22]. Nevertheless, the translational value of such simulations is inherently constrained by necessary simplifications in parameters, material properties, and boundary conditions [23].

Recent techniques have leveraged digital model superimposition to analyze crown centroid displacement before/after occlusal loading, providing a non-contact, non-invasive proxy to infer the effects associated with the anterior component of force (ACF) [24, 25], as crown movement under occlusal loading is driven by bite force components including ACF. Building upon our research group further established mesiodistal reference lines in the contact area of the target tooth position to measure the changes in the contact area before and after occlusion [26, 27] (Fig. 1F).

This study uses digital model measurement to quantify changes in centroid position and inter-tooth contact area between the first molar implant and its mesial adjacent tooth pre- and post-occlusion. These geometric changes are used as indirect indicators to evaluate ACF-related occlusal effects (rather than direct quantification of ACF force itself). Ultimately, this research aims to provide data to inform standardized and personalized preventive strategies for improving implant long-term outcomes.

Materials and methods

Ethical approval for this observational study was obtained from Ethics Committee of Shanxi Medical University Hospital of Stomatology (Approval No. 2024SLL017). Participants were consecutively enrolled based on the following inclusion criteria: age between 25 and 60 years; requirement for an implant-supported restoration due to a missing first molar; absence of temporomandibular joint disorders (e.g., TMD or ankylosis); and the ability to provide informed consent for non-interventional, long-term follow-up. Exclusion criteria included incomplete opposing dentition; teeth adjacent to the implant site with mobility reaching or exceeding Miller grade I (horizontal movement amplitude ≥ 0.1 mm), as well as those confirmed by clinical and radiographic examination to have ankylosis between the tooth root and alveolar bone.;presence of parafunctional habits such as bruxism; a diagnosed temporomandibular joint disorder; or an opposing arch restored with removable partial or complete dentures.

A total of 78 participants, representing 90 implant-supported restorations for missing first molars, were enrolled according to predefined inclusion criteria and sample size calculations. All participants provided written informed consent prior to enrollment. Surgical and prosthetic procedures were conducted between April 2024 and January 2025 at the Department of Implantology, Shanxi Medical University Hospital of Stomatology. To ensure consistency in treatment protocols, a single implant system (Straumann; Straumann AG) and CAD/CAM-fabricated zirconia crowns (Lava Plus; 3 M) were used uniformly across all cases. All prosthetic interventions were performed in accordance with a standardized clinical protocol.

Following definitive seating, adjustment, and polishing, each restoration was evaluated using two established baseline criteria. First, occlusal contacts were refined until a 12-µm shim stock film (Arti-Fol metallic shimstock-film; Bausch) could be smoothly withdrawn under light pressure in the maximum intercuspal position [28]. Second, proximal contacts were considered acceptable when dental floss (Essential Floss; Oral-B) passed through with noticeable resistance but without tearing, while a 30-µm metal feeler gauge (STANLEY; Stanley Black & Decker) could not be inserted in the buccolingual direction [29].

Immediately following restoration, each subject underwent intraoral scanning and measurement of the change in centroid position before and after occlusion (Δd_C) and the change in the proximal contact gap before and after occlusion (Δd_P). Six months after restoration, a follow-up assessment was conducted to measure the increment in proximal contact gap (ΔD) using a metal feeler gauge. The flowchart of the study protocol is shown in Fig. 2.

Fig. 2.

Flowchart of study protocol

Bite force training

Subjects were instructed to perform voluntary tooth clenching at the intercuspal position (ICP) with their habitual bite force. This standardized procedure is widely used in clinical practice for intermaxillary registration and objective assessment of occlusal stability. Occlusal imprints were recorded using 100 μm-thick articulating papers (BK51/BK52, Bausch & Lomb), alternating between red and blue to enhance contrast. ICP stability was considered acceptable only if three consecutive imprints demonstrated identical functional tooth contacts (e.g., on first molars or premolars). Subjects were excluded if this criterion was not met, as indicated by inconsistent contact locations or absence of key functional contacts.

Acquisition of intraoral scan data

The intraoral 3D scanner (Aoralscan 3; SHINING 3D) was employed to acquire high-fidelity surface data of the dentition, as well as buccal occlusion records. All intraoral scans were performed following a standardized acquisition protocol. Digital impressions, capturing the clinical crowns and gingival margins, were systematically acquired from the first premolar to the second molar in both the maxillary and mandibular dental arches. Subsequently, static occlusion was recorded by scanning each participant as they closed into the maximum intercuspal position (MIP) using their natural, habitual biting force. All datasets were exported in Standard Tessellation Language (.stl) format. To ensure procedural uniformity and optimal data quality, all scans were performed by a single, trained operator. Intraoral scan data were collected following a standardized protocol to ensure accuracy and consistency.

Data preprocessing

The .stl files derived from intraoral scans were preprocessed using Geomagic Wrap 2021 software (3D Systems, USA). The procedure began with the segmentation of the first molar (FM) and second premolar (SP) into individual digital models, accomplished by accurately tracing the crown boundaries along the gingival margin and adjacent anatomical contours (Fig. 3A). Subsequently, a patient-specific coordinate system was established based on key anatomical landmarks of the implant-supported crown. The occlusal plane (OP) was defined by fitting a best-fit plane to the region of maximum curvature on the occlusal surface of the molar (Fig. 3B/C). With the origin located at the centroid of the crown (C6) (Fig. 3D), the Z-axis was oriented perpendicular to the OP. The Y-axis was aligned along the buccolingual line connecting the occlusal extremities of the proximal contact area (Fig. 3E), thereby positioning the OP within the XY-plane, while the X-axis was directed mesially (Fig. 3F).

Fig. 3.

Data preprocessing steps for the first molar. A Delineation of crown margins and individual tooth segmentation. B Curvature map of the first molar. C Occlusal plane (OP) fitted to the region of maximum curvature. D Location of the crown centroid (C6). E Definition of reference line Y connecting the buccal and lingual boundaries of the mesial contact area. F Establishment of the local coordinate system with its origin at C6, Y-axis aligned with line Y, and Z-axis perpendicular to the OP, the x-axis is oriented mesially

Measurement of Δd_P

First, a reference line is drawn 0.1 mm above the proximal contact area (PCA) occlusal boundary within the proximal contact area between the FM and the SP (Fig. 4A). Next, boundary lines were drawn on the buccal bite data of the target teeth and projected onto SP_copy and FM_copy, which were produced from SP and FM duplicating, respectively. The buccal scanning data within the boundary lines was regarded as the common area. The SP_copy and FM_copy were registered to buccal bite data respectively through the “Best Fit Alignment” function according to the common area. After alignment, SP_copy and FM_copy were renamed SP_bite and FM_bite to represent the complete surface data of the target teeth under bite force, respectively (Fig. 4B). Subsequently, reference lines are extracted from both the original and occlusally registered models (Fig. 4C) and sampled at 0.5 mm intervals to generate corresponding point pairs (P6–P5) and (P6_bite–P5_bite) (Fig. 4D), respectively. Finally, the mesiodistal (X-axis) distances for each pair of corresponding points in (P6–P5) and (P6_bite–P5_bite) are calculated to determine the mesiodistal distance in the open-mouth position (d_o)_n and the occlusal position (d_b)_n. The difference in mesiodistal distance for each point pair before and after occlusion is computed as Δd_Pn (Fig. 4E). The arithmetic mean of these Δd_Pn values represents Δd_P.     

Fig. 4.

Measurement procedure for the change in the proximal contact gap before and after occlusion (ΔdP) A Placement of reference lines (L5, L6) on the proximal surfaces of the second premolar (SP) and first molar (FM). B Occlusal registration using the common buccal region to align pre- and post-occlusion models. C Extraction of reference lines from both pre-occlusion (brown) and post-occlusion (blue) models. D Sampling of corresponding point pairs (P5-P6) along the reference lines. E Calculation of Δdpn as the difference in inter-point distances before (d_on) and after (d_bn) occlusion

Measurement of Δd_C

The centroids of the crowns of the first molar and the second premolar were identified in both the initial and occlusal states, resulting in (C5–C6) and (C5_bite–C6_bite), respectively. The mesiodistal distances of (C5–C6) and (C5_bite–C6_bite) were then calculated to obtain dcom and dcom_bite. Finally, Δd_C was determined,.

To ensure data reliability, each scan dataset was measured three times. The mean value of all measurements was used for statistical analysis.

Biomechanical index assessment were each performed by a single operator who had completed standardized training. All operator-dependent steps—including digital model segmentation, registration of pre- and post-occlusion scans, placement of mesiodistal reference lines within the interdental contact area, and quantification of centroid displacement and inter-tooth contact area changes—were carried out independently by this same certified operator to ensure procedural consistency. The masurement flowchart of the study protocol is shown in Fig. 5.

Fig. 5.

The masurement flowchart of the study protocol

Measurement of ΔD

The proximal contact gap (D, µm) is defined as the thickness of the biggest metal feeler gauge (with scale of 30, 40, 50…, 100 μm) that can be inserted through the contact point with resistance. The gap must be too narrow to accommodate the next larger gauge. The measurement taken immediately after restoration served as the baseline value (D₀ = 20 μm). The measurement obtained at the 6-month follow-up was designated D₆, and the change over time was calculated as .

To determine the gap values under varying contact conditions, three assessors concurrently performed measurements using dental floss and a metal feeler gauge to establish a consistent reference standard. (Detailed methodological procedures are provided in Supplementary Material 1.) Based on the recorded proximal contact gap size (D₆) at the 6-month follow-up, the samples were categorized into three groups: tight (20–30 μm), loose (40–50 μm), and open (> 50 μm).

Statistical analysis

Sample size calculation: The sample size was determined using PASS 2021 software (NCSS, LLC) based on a multiple linear regression model, with a significance level of α = 0.05 and a desired statistical power of 1 − β = 0.8. The number of predictor variables was set to 3. An effect size (f²) of 0.67 was assumed, as estimated from a pilot study (n = 20). Under these parameters, the minimum required sample size was calculated to be 32. Accounting for a projected dropout rate of 10%, a total of at least 36 participants were planned for inclusion in the study.

Data management and statistical analyses were conducted using SPSS 27.0 (IBM) and R 4.5.2 software. Normality of continuous variables was assessed using the Shapiro-Wilk test. Categorical variables are presented as frequency and percentage [n (%)]. Continuous variables that met the assumption of normality are reported as mean ±standard deviation (± s), whereas non-normally distributed variables are summarized as median and interquartile range [M (P25, P75)]. To identify factors influencing ΔD, chi-square tests, one-way ANOVA, binary logistic regression, and two-way ANOVA were employed. A restricted cubic spline (RCS) regression model was fitted to examine the nonlinear relationship between ΔD and mechanical indicators over the follow-up period. Model predictive validity was evaluated using Cohen’s Kappa coefficient.

Results

This study included a total of 78 subjects (30 males and 48 females) with a mean age of 41.39 ± 13.36 years, comprising 90 first molar implant restorations. The 6-month follow-up results showed that the incidence of PCL in implant restorations was 17.78% (16/90), while the rate of changes in proximal contact status (weakening or loss of proximal contact strength) was 48.89% (44/90). In the analysis of influencing factors, age and implant position (maxillary/mandibular) showed no statistically significant differences in their impact on the proximal contact status of implants (P > 0.05). However, the sex factor showed a significant influence (χ² = 7.48, P = 0.024), with male patients exhibiting a higher rate of adjacent segment status change (63.63%) compared to females, but a lower incidence of PCL (15.15%) than female patients (Table 1).

Table 1.

Baseline demographic and clinical characteristics of the study participants

	Tight(n = 46)	Loose(n = 28)	Open(n = 16)	χ² / F	P
Sex
Male	12(36.36%)	16(48.48%)	5 (15.15%)	7.48a	0.024*
Female	34(59.65%)	12(21.05%)	11(19.30%)
Location
Maxilla	14(41.18%)	12(35.29%)	8 (23.53%)	2.38a	0.304
Mandible	32(57.14%)	16(28.57%)	8 (14.29%)
Age (y)	39.78 ± 12.77	41.39 ± 13.93	44.50 ± 11.21	0.80b	0.451
Biomechanical index
ΔdP > 0 μm	10 ± 7	22 ± 8	41± 8	145.96b	< 0.001***
ΔdP < 0 μm	−14 ± 10	−27 ± 5	−30 ± 4
ΔdC > 0 μm	33 ± 19	54 ± 29	47 ± 36	37.99c	< 0.001***
ΔdC < 0 μm	−33 ± 21	−36 ± 34	−59 ± 30

^a Chi-square Test was used to determine the influence of sex and implant position on proximal contact status

^b One-way ANOVA was applied for comparing the effects of age and Δd_P on proximal contact status

^c Welch’s ANOVA was employed to compare the effect of Δd_C on proximal contact statu, the test results show that when Δd_C < 0 μm, the data in the Loose group exhibit slight skewness, but it is statistically insufficient to reject the normality hypothesis, representing non-normality within acceptable limits

*P < 0.05; ***P < 0.001

Further investigation showed the biomechanical index (Δd_P / Δd_C) differed significantly in evaluating adjacent state changes. Intergroup differences in Δd_P were highly significant (F = 145.96, P < 0.001). Scheffé’s post hoc test revealed most pairwise comparisons were significant (P < 0.01 or P < 0.05). When Δd_P > 0 μm, the tight group was significantly lower than both loose and open groups (both P < 0.001), and the loose group was significantly lower than the open group (P < 0.001). Indicating higher Δd_P values correlate with greater likelihood of adjacent state change. When Δd_P < 0 μm, the tight group remained significantly higher than loose (P = 0.005) and open (P = 0.049), but no significant difference was found between loose and open (P = 0.995) (Fig. 6A). In contrast, although Δd_C differed significantly across groups (Welch F = 37.99, P < 0.001). Tamhane’s T2 test showed no significant pairwise differences at any threshold (P > 0.05) (Fig. 6B).

Fig. 6.

Distribution of Δd_P and Δd_C. A Displays the distribution of Δd_P across the three groups. Δd_P values below 0 μm are classified as PCA−, whereas values above 0 μm are classified as PCA+. B Presents the distribution of Δd_C among the three groups. Δd_C values below 0 μm are designated as COM−, and those above 0 μm as COM+. Group differences were assessed using letter-based annotation: groups sharing the same letter do not differ significantly, while groups labeled with different letters exhibit statistically significant differences

A multivariate Binary Logistic Regression Analysis with sex, Δd_P, and Δd_C as independent variables, with the binary outcome (change vs. no change in proximal contact status) serving as the dependent variable (Table 2). The findings showed Δd_P significantly affected proximal contact status (P < 0.001). Just to be clear, for every 1 μm increase in Δd_P the odds of change in proximal contact status increases 5.2%. Moreover, sex had a significant effect on the outcome (P = 0.001), and females had only 14% of the odds of change than males. On the other hand, Δd_C produced no significant effect (P = 0.873). The equation employs a calculation formula: In which p indicates the probability of no change in proximal contact and 1-p probability of change.

Table 2.

Binary logistic regression results

	β	S.E.	z	Wald χ²	P	OR	95% CI
Sex	−1.98	0.61	−3.25	10.57	0.001**	0.14	0.04 ~ 0.46
ΔdP	0.05	0.01	3.61	13.04	< 0.001***	1.05	1.02 ~ 1.08
ΔdC	−0.00	0.01	−0.16	0.03	0.873	1.00	0.99 ~ 1.01

**P < 0.01; ***P < 0.001

To further investigate the influence of biomechanical factors in different directions on the proximal contact status, the Aligned Rank Transform (ART) ANOVA was used to examine the relationship between two biomechanical indices (Δd_P / Δd_C) and outcome indices (ΔD). The analysis revealed a significant main effect for Δd_P (F = 7.81, P = 0.006) and a significant interaction between Δd_P and Δd_C (F = 8.17, P = 0.005), but no significant main effect for Δd_C itself (F = 1.42, P = 0.236) (Table 3). This indicates that the average effect of Δd_C on ΔD across all Δd_P levels was near zero. Yet, this “average null effect” arises from opposing effects under different conditions, not a true lack of influence. This also explains why Δd_C lacked significant independent predictive power in the logistic regression analysis. Further simple effect analysis showed that when Δd_P > 0 μm, the difference in Δd_C between the two groups was significant (t = − 3.32, P = 0.001); when Δd_P < 0 μm, the difference was not significant (t = 1.05, P = 0.296). These results suggest distinct movement patterns of natural teeth after force application: positive Δd_P and Δd_C indicate mesial bodily movement of the adjacent tooth, while opposite signs suggest primarily complex rotational movement.

Table 3.

Effect of the biomechanical index (Δd_P /Δd_C) on ΔD

	SS	df	MS	F	P	Partialη2
Δd	4078.62	1	4078.62	7.81	0.006**	0.08
ΔdC	743.35	1	743.35	1.42	0.236	0.02
ΔdP × ΔdC	4267.59	1	4267.59	8.17	0.005**	0.09

**P < 0.01

Taken together, Δd_P is the core variable for assessing the proximal contact status of dental implants. To visually demonstrate the relationship between Δd_P and ΔD, an RCS model was established using 70 samples with Δd_P as the independent variable and ΔD as the dependent variable. After covariate adjustment, the results revealed a significant nonlinear relationship between Δd_P and ΔD (Nonlinear P < 0.001, Overall P < 0.001). As Δd_P increased, ΔD initially decreased rapidly, but the rate of decline gradually slowed until reaching a minimum point before rebounding, ultimately forming a “J-shaped” trend. Based on this trend, clinically significant intervals can be defined. When Δd_P ∈ [− 13,9] µm, ΔD ≤ 10 μm, indicating stable adjacent relationships during follow-up; when Δd_P∈ [− 28, − 13) or (9,30] µm, ΔD ranges between 10 and 30 μm, suggesting weakened but still existing adjacent contact; when Δd_P∈ (30,42] µm, ΔD > 30 μm, marking the occurrence of PCL (Fig. 7).

Fig. 7.

RCS model for ΔD. In the figure, the purple-shaded area represents unchanged proximal contact status; the blue-shaded area indicates weakened but still contacting proximal strength; the red-shaded area corresponds to loss of proximal contact

The other 20 samples served to validate the model. Therefore, model validation was achieved. The results reveal that the model has a high goodness of fit (κ = 0.59, P = 0.003).

Discussion

The methodological approach of this study draws on the operational definitions of ACF/PCF established in prior work [18, 20]. Zhao et al. [30] extended this approach by developing a three-dimensional analytical framework that combines dynamic occlusal force mapping with high-precision intraoral scan data, resolving occlusal forces into mesiodistal, buccolingual, and occlusogingival components. Their analysis revealed that in interproximal regions exhibiting clinical food impaction, the mesially directed force component on the distal tooth was significantly reduced. This finding suggests a potential relationship between the mesiodistal force ratio and the degree of proximal contact gap widening. To minimize confounding effects, subjects with notable periodontal abnormalities were excluded. This exclusion criterion was implemented to help ensure that the observed pre- and post-occlusal changes in interproximal relationship more directly reflect mechanical loading effects. Consequently, using this change as an indirect measure of ACF/PCF-related biomechanical effects is methodologically justified.

In selecting the occlusal loading protocol, this study avoided the maximum voluntary bite force (MVBF)—a measure with well-documented poor intra-subject repeatability [31]—and instead adopted the habitual bite force, which demonstrates stable output following standardized instruction and practice [32, 33]. Prior evidence shows that this approach yields a markedly lower within-subject coefficient of variation [26], confirming its measurement stability. To ensure consistency, all participants underwent identical instruction and standardized practice prior to scanning, thereby enhancing both the technical repeatability and biological fidelity of the resulting mechanical parameters.

In selecting the scanning protocol, a targeted 4-unit local scanning strategy was employed. This decision is supported by evidence indicating that local scanning (within 3 units) yields significantly higher trueness and precision compared to hemi-arch or full-arch protocols [34]. Although the performance of the specific scanner used (SHINING Aoralscan 3) in local-scan mode has not been independently validated, its predecessor (first-generation Aoralscan) demonstrated trueness and precision within 5 μm under comparable conditions [35]. Given the continuity in core hardware architecture, the Aoralscan 3 is reasonably expected to exhibit at least equivalent performance. To ensure consistency, all intraoral scans were performed by operators who had completed a standardized training and certification program. Subsequent digital measurements were conducted exclusively in Geomagic Wrap 2023. The systematic error associated with the occlusal registration process was estimated to be 10–20 μm, which is consistent with values reported in prior studies using similar methodology [25, 27]. To mitigate random measurement error, each STL model was measured independently three times by a single, standardized-trainee researcher.

This study did not evaluate inter-operator repeatability. However, our prior validation study demonstrated that—despite inherent subjectivity in operator-dependent steps such as digital model segmentation and reference line placement—standardized training significantly mitigates inter-observer variability, yielding high intra-class correlation coefficients (ICCs) for key distence measurements (the ICC values of the three operators ranged from 0.800) [27]. These findings support the established reliability and measurement validity of the digital model analysis protocol used herein.

The digital model measurement technique employed in this study features a well-defined procedural workflow and transparent data interpretation protocol. And the hardware (Shining Aoralscan 3 intraoral scanner) employed for data acquisition and dimensional measurement in this study are routinely adopted in academic and clinical research settings.The commercial software Geomagic Wrap 2021 is readily accessible, which is also an advantage of this method in application. Among existing assessment methods, Δd_C simplifies tooth movement by representing overall displacement through a single centroid, conferring operational simplicity [25]. However, this approach captures only limited dimensional data and fails to reflect the complex three-dimensional dynamics of natural teeth—particularly rotational displacements during functional loading—thus inherently constraining its ability to predict clinical outcomes. In contrast, Δd_P specifically evaluates displacement changes at the proximal contact area, enabling a more direct, localized, and sensitive assessment of biomechanical responses under occlusal load. This targeted sensitivity is precisely why Δd_P exhibits superior predictive accuracy compared to Δd_C.

Δd_P was defined as the mesiodistal difference in the interproximal space of the target teeth before and after occlusion, which represents the relative displacement of the adjacent teeth relative to the implant. The rationale for using this parameter as an indirect measure of ACF/PCF on natural teeth is based on two premises. First, the implant is osseointegrated with the alveolar bone, and its physiological displacement under functional loading is minimal, approximately one-tenth that of natural teeth [36]. Therefore, Δd_P is considered to approximate the physiological movement of the natural teeth. Second, periodontal status was controlled; all included subjects met strict periodontal health criteria (alveolar bone resorption not exceeding one-third of the root length and tooth mobility less than grade I to ensure that the observed displacement was primarily driven by horizontal occlusal force rather than compromised periodontal support. The results showed that when Δd_P exceeded 9 μm, the interproximal space increased during the 6-month follow-up, indicating that the natural teeth were subjected to a horizontal force dominated by ACF, consistent with the mechanical role of ACF in promoting mesial drift. When Δd_P was between —13 μm and 9 μm, no significant changes in proximal contacts were observed, suggesting a balance between ACF and PCF. Notably, when Δd_P was less than —13 μm, the interproximal space also showed a significant increasing trend during follow-up. This may have been due to excessive PCF pushing the natural teeth distally, which could accelerate proximal wear. Studies have indicated that zirconia‑based restorations can exacerbate enamel wear of opposing or adjacent natural teeth [37], thereby promoting the formation of proximal spaces.

As a preliminary exploratory work, this study requires cautious interpretation of its conclusions in consideration of the following methodological limitations. First, the relatively limited sample size (n = 90) and overrepresentation of females in the cohort may, to some extent, restrict the generalizability of the findings and introduce potential bias into the estimation of effects for predictors such as gender. Second, limitations exist in the measurement procedures. The single-acquisition strategy employed for intraoral scanning has a systematic error (approximately 5 μm) that overlaps with the clinical threshold range of the Tigh group (—13 to 9 μm), which could systematically reduce the detection sensitivity of the regression model for subtle tooth displacements; the insufficient resolution of the metal feeler gauge prevents precise quantification of proximal contact gap changes smaller than 10 μm, and the resulting measurement error may compromise the relationship between Δd_P and the long-term mechanical effects of ACF/PCF; additionally, tooth mobility assessment relies on subjective clinical visual inspection and manual probing, and the low sensitivity of this approach [38] may undermine the explanatory power of Δd_P for ACF/PCF. Third, regarding study design, the 6-month follow-up period is inadequate to sensitively capture early dynamic changes in interproximal opening and to assess its long-term evolutionary trends; moreover, bite force data are derived from a single record of habitual bite force, failing to account for individual variations in bite force amplitude, direction, and duration, which may introduce errors into the constructed model.

Future studies should expand the sample size and adopt a gender-balanced design, while implementing a series of methodological optimizations: conducting repeated intraoral scans (≥ 3 times) and using the intraclass correlation coefficient to evaluate scanning errors; employing a dental mobility meter to objectively quantify inclusion criteria; and exploring higher-precision micron-level interproximal gap measurement techniques. Concurrently, future research should incorporate longer-term follow-up (12 to 24 months) and multiple assessment time points (1, 3, 6, and 12 months) to comprehensively evaluate the quantitative relationship between ACF/PCF and PCL; and more comprehensive, dynamic bite force data should be collected when feasible, to systematically validate and deepen the quantitative relationship between ACF/PCF and PCL initially uncovered in this study.

Although this study protocol has limitations, the findings remain informative: Δd_P reflects the reversible elastic displacement of natural teeth under a single application of ACF, whereas the long-term effect of ACF may induce mesial drift, leading to proximal contact loss (PCL). The 6-month follow-up data showed that participants with Δd_P > 9 μm or Δd_P <—13 μm had already exhibited changes in proximal contact status, suggesting that short-term mechanical responses may serve as a potential predictor for long-term drift. This study provides preliminary biomechanical evidence regarding the mechanism of ACF-mediated tooth movement and offers a methodological reference for future research design.

Conclusion

Within the limitations of this study, we indirectly evaluated the effects related to ACF/PCF through digital model measurement techniques and confirmed their relationship with the PCL of dental implants. Quantitative analysis further revealed a significant nonlinear relationship between Δd_P and ΔD at the 6-month follow-up after implant-supported restoration: when Δd_P ranges from − 13 to 9 μm, proximal contact remains stable; conversely, PCL occurs.

Supplementary Information

Supplementary Material 1. ^{(57.9KB, docx)}

Abbreviations

PCL

Proximal contact loss

ACF

Anterior component of force

PCF

Posterior component of force

Δd_P

The change in the proximal contact gap before and after occlusion

Δd_C

The change in centroid position before and after occlusion

ΔD

The increment in proximal contact gap during the 6-mouth follow-up period

PCA+

ΔdP > 0 μm

PCA−

ΔdP < 0 μm

COM+

ΔdC > 0 μm

COM−

ΔdC < 0 μm

MIP

Maximum intercuspal position

OP

Occlusal plane

FM

First molar

SP

Second premolar

Authors' contributions

Feng Wu, Derong Yin, Meie Jia, Lingrui Gao: Contributed to conception and design of the study. Lingrui Gao, Lijun Xue, Zhongda Wang, Hongwei Gao: Contributed to data acquisition. Lingrui Gao: Contributed data analysis. Derong Yin, Lingrui Gao: Contributed to statistical analysis, interpretation, and manuscript drafting. All authors critically revised the manuscript and gave final approval for submission.

Funding

This study was Supported by Postgraduate Education Innovation Program of Shanxi Province (No.2025JG072), Start-up Fund for Doctor of Shanxi Medical University (No. XD2323) Fundamental Research Program of Shanxi Province (No.202403021212214, 202403021222216), Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No. 2024L106, 2024L107), and Project of Clinical Research Center of Shanxi Province Clinical Medical Research Center for Oral Diseases (Maxillofacial Deformities) (No.LCZX0008).

Data availability

The data that supports the findings of this study are available from the corresponding author, upon reasonable request.

Declarations

Ethics approval and consent to participate

This study was approved by the Ethics Committee of Shanxi Medical University Hospital of Stomatology (Approval No. 2024SLL017 ). All procedures involving human participants adhered to the ethical standards of the institutional and/or national research committee and complied with the Declaration of Helsinki and its later amendments or equivalent guidelines. Informed consent was obtained from all participants or their legal guardians.

Consent for publication

Informed consent was obtained from all subjects and/or their legal guardian(s).

Competing interests

The authors declare no competing interests.