Trabeculae microstructure parameters serve as effective predictors for marginal bone loss of dental implant in the mandible

Marginal bone loss (MBL) is one of the leading causes of dental implant failure. This study aimed to investigate the feasibility of machine learning (ML) algorithms based on trabeculae microstructure parameters to predict the occurrence of severe MBL. Eighty-one patients (41 severe MBL cases and 40 normal controls) were involved in the current study. Four ML models, including support vector machine (SVM), artificial neural network (ANN), logistic regression (LR), and random forest (RF), were employed to predict severe MBL. The area under the receiver operating characteristic (ROC) curve (AUC), sensitivity, and specificity were used to evaluate the performance of these models. At the early stage of functional loading, severe MBL cases showed a significant increase of structure model index and trabecular pattern factor in peri-implant alveolar bone. The SVM model exhibited the best outcome in predicting MBL (AUC = 0.967, sensitivity = 91.67%, specificity = 100.00%), followed by ANN (AUC = 0.928, sensitivity = 91.67%, specificity = 93.33%), LR (AUC = 0.906, sensitivity = 91.67%, specificity = 93.33%), RF (AUC = 0.842, sensitivity = 75.00%, specificity = 86.67%). Together, ML algorithms based on the morphological variation of trabecular bone can be used to predict severe MBL.


Results
Trabecular microarchitecture changes in severe MBL cases. Eighty-one subjects were included in this study, and 41 were identified severe MBL of dental implants. Gender (P = 0.007), cortical bone thickness (P = 0.007), and smoking (P = 0.008) showed a significant difference between the severe MBL cases and the normal controls (Supplementary Table S1). Morphological variables of the peri-implant and the normal adjacent alveolar bone were also compared between the severe MBL cases and the normal controls. Structure model index (SMI) (P = 0.007) and trabecular pattern factor (Tb.Pf) (P = 0.017) significantly increased in peri-implant alveolar bone of severe MBL cases (Fig. 1). Percent bone volume (BV/TV) (P = 0.002), trabecular number (Tb.N) (P = 0.025), and intersection surface (I.S) (P = 0.030) significantly increased in peri-implant alveolar bone of normal controls (Fig. 1). Additionally, we analyzed preoperative trabecular microarchitecture parameters of all subjects at T 0 , and there was no difference between the two groups. The results of trabecular microarchitecture variables at T 1 and T 0 was exhibited in Supplementary Tables S2 and S3.
Morphological variables and their role in predicting MBL. Inspired by the above findings, we analyzed all variables using principal component analysis and correlation covariance matrices. All results relevant to morphological variables were confirmed with a significant difference and reasonable collinearity. SMI, Tb.Pf, Tb.N, bone surface volume ratio (BS/BV), and BV/TV manifested a higher correlation with MBL, while other morphological variables could not bring a noteworthy contribution. Figure 2 reflected the ordination and contribution of all variables, along the first two "Multiple Factor Analysis" (MFA) components. The components explained 47.2% of the total variance in the data. Morphological parameters located in component 1 made significant contributions to the principal component, and all clinical parameters distributed in component 2.
The logically obvious correlation between morphological parameters was shown in Fig. 3, and almost all correlation coefficients reached remarkably significant levels. Meanwhile, the linearity and credibility of trabecular bone microparameters were verified. SMI (P = 0.002) and Tb.Pf (P = 0.0165) exhibited a significantly high positive correlation with MBL. However, BV/TV and BS/BV manifested a negative correlation with MBL. Gender (P = 0.007), cortical bone thickness (P = 0.0072), and smoking (P = 0.0079) were powerfully correlated with MBL.
Performance of ML models. Based on the consequence of correlation analysis, we eliminated some meaningless variables to build ML models. Each model was superior to a single factor predictor. The SVM model performed the best (AUC = 0.967), followed by ANN (AUC = 0.928), LR (AUC = 0.906), RF (AUC = 0.842), SMI alone (AUC = 0.705), Tb.Pf alone (AUC = 0.663), and BV/TV alone (AUC = 0.629) (Fig. 4, Table 1). As the best Figure 1. Comparison of morphological parameters among the peri-implant and normal adjacent alveolar bone in cases and controls. In severe MBL cases, SMI and Tb.Pf showed the visible difference between the periimplant and normal adjacent alveolar bone. BV/TV, Tb.N, and i.S exhibited a significant difference between the peri-implant and normal adjacent alveolar bone in normal controls.

Scientific Reports
| (2020) 10:18437 | https://doi.org/10.1038/s41598-020-75563-y www.nature.com/scientificreports/ model, the SVM's sensitivity and specificity were 91.67% and 100.00% at its optimal cutoff, respectively. SVM also presented a perfect optimal criterion (0.917), satisfied positive (1.000) and negative (0.938) predictive values, the maximum positive diagnose-likelihood-ratio (Infinite), and the minimum negative diagnose-likelihood-ratio (0.083). Moreover, the SVM model had the smallest false positivity and false negativity. The cutoff value of SMI was 1.027, while the corresponding sensitivity and specificity were 65.85% and 67.50%, respectively. The cutoff value of Tb.Pf was 0.968, and the sensitivity and specificity were 63.41% and 62.50%, respectively. We listed the performance of each model in Table 2. Based on the RF model, we rearranged the variables according to the importance of predicting MBL measurement through the Gini index (Fig. 5).

Discussion
Due to the important role of MBL in dental implant failure, MBL have become an essential clinical examination in postoperative follow-up. The purpose of this study was to verify that ML algorithms combined with early-stage trabecular bone variables could predict MBL more effectively than conventional methods. Our results showed a great performance of ML methods for predicting MBL, which can be considered as the feasible early warning for severe MBL. It was noted that the other factors resulting in MBL should be taken into account in future studies. Previous researches about MBL mainly concentrated on the cause and treatment 6,9,12,13,22,23 , but rarely on the prediction of MBL 15 . Factors such as trabecular bone microstructure parameters possibly affecting MBL during bone remolding have been well elucidated 15 , but the role of trabecular bone in this progression remains unclear. To our knowledge, this is the first study to establish and validate ML models based on trabecular microstructure parameters to predict the occurrence of MBL of the submerged dental implant in mandible.
It has been widely acknowledged that various factors, including cortical bone thickness, smoking, periodontitis, SMI, Tb.Pf, and BV/TV, function as a complex to cause MBL 8 . Previous studies have also demonstrated that the proportion of cancellous bone 10 , crown-to-implant ratio 24 , bone texture, and cortical width 15 , are risk factors of MBL. Therfore, single predictive factor cannot accurately predict MBL because MBL is a multifactorial outcome. One recent study attempted to employ Cox regression and mixed linear modeling to predict the occurrence of MBL, but they aimed to assess interventions and their consequences with regard to further bone loss at sites diagnosed with peri-implant inflammation 25 . Another study incorporated several radiographic features of cortical and cancellous bone texture, cortical width, and patient smoking habits to build a statistical model to predict MBL with a sensitivity of 62.1% and specificity of 67.5% 15 . Compared to conventional statistical methods, the current study verified that ML algorithms predicted MBL more accurately. Of note, the SVM model performed best with a sensitivity of 91.67% and specificity of 100.00%, which was significantly better than that of SMI, Tb.Pf or BV/TV alone.
To demonstrate the differences and correlations of morphological variables between the controls and severe MBL cases, we also analyzed morphological variables of trabecular bone in patients with MBL during bone remolding. At the early stage of functional loading, CBCT analysis exhibited a worse outcome of SMI and Tb.Pf in peri-implant alveolar bone of severe MBL cases. These findings revealed that severe MBL cases demonstrated the premonitory morphological variation in trabecular microarchitecture at the early stage. Consistent with our results, a previous study reported that the preservation and improvement of trabecular microarchitecture always brought about a better therapeutic benefit for osteoporosis at multiple skeletal sites 26 . SMI and Tb.Pf were the best determinants of the MBL level, which they reflected the structure quality of the trabecular bone Although the current study has demonstrated that ML could predict the occurrence of MBL more effectively than conventional methods, some limitations need to be acknowledged. Due to the proximity of the measurement point to the implant root, implant artifacts remain unavoidable. The variables in the current study lacked results of the periodontal examination, such as probing depth. Additionally, this study was limited to patients who received implant treatment in mandible. Further studies on larger sample sizes using more relative variables (e.g. periodontal or microbiological) might be better for the ML performance. At last, a mean 20.95 ± 2.67 months of follow-up after functional loading was also limited to predict MBL. Hence, we entitled this study as a preliminary one.
In conclusion, the current study verified that the severity of early bone resorption was closely related to trabecular microarchitecture during the early stage of functional loading. Change of trabecular microarchitecture can provide an early warning for severe MBL. ML models SVM, ANN, LR, and RF indicate superior performance compared to the single predictor in predicting MBL of mandibular implant.

Methods
Study design. To address the research purpose, we designed and implemented a cross-sectional study. All    www.nature.com/scientificreports/ ning voltage and current were 110 kV and 10 mA, while exposure and scanning times were 3.6 s and 18 s. We reconstructed the original radiographs using the center of the implant in the sagittal, coronal, and transverse plane. The implant length and diameter were used to test the accuracy of reconstructed images. MBL measurement was performed as follows: (1) the horizontal interface between implant and abutment was validated as the reference loci; (2) vertical distances from the loci to the most coronal level of bone to implant contact at the Table 2. Performance of each model at optimal cutoff point. The optimal cutoff was considered as the point maximizing the sum of sensitivity and specificity.  www.nature.com/scientificreports/ mesial and distal sites were measured at the preceding time points 27,28 ; (3) analysis of radiographs was conducted by two investigators who did not participate in this study. We obtained the maximum MBL of the implant at T 1 and T 2 as the corresponding MBL level (Supplementary Fig. S1). According to the T 2 MBL level, we divided all subjects into two groups:

Model Sensitivity (%) Specificity (%)
-Normal controls less than 2 mm MBL in the first year after fixed prosthesis, then less than 0.2 mm MBL per year -Severe MBL cases MBL level exceeding normal controls Measurement of peri-implant bone morphological parameters. We imported the T 1 radiographs to CT Analyzer (CTAn, SkyScan, Antwerpen, Belgium). The threshold value of binary selection was determined by completely distinguish cortical bone and trabecular bone (Supplementary Fig. S2a). We confirmed the region of interest (ROI) by the diameter of each implant. We selected five sequential ROI layers adjoining the implant root as the volume of interest (VOI) of peri-implant alveolar bone (Supplementary Fig. S2b). Another five sequential ROI layers away from the implant were chosen as VOI of the normal adjacent alveolar bone (Supplementary Fig. S2b). The trabecular bone morphological parameters, such as SMI, Tb.Pf, BV/TV, i.S, and Tb.N were extracted using three-dimensional analysis of each VOI. SMI, Tb.Pf, and i.S represent the shape and quality of trabecular bone. BV/TV and Tb.N usually mean quantity of trabecular bone. Finally, we calculated morphological variables by the ratio of peri-implant to normal adjacent alveolar bone.

PCA analysis.
Including clinical and morphological parameters, all variables were utilized for ordination analysis and contribution degree evaluation of principle component using the "Multiple Factor Analysis" (MFA) function in the R package "FactoMineR". As a dimensionality reduction method, MFA reduces the complexity of multivariate data and allows visual interpretation of significant patterns. It is suited to data that contains both continuous and categorical variables. MFA also allows grouping of variables where each group is normalized individually to balance their influence. An MFA correlation circle plot depicts the continuous variables, and the factors plot depicts the categorical variables.

Visualization of correlation and covariance matrices. Correlation and covariance matrices can visu-
alize the patterns and relationships between the variables. We had twenty original variables, including object variable MBL. The visualization of matrices re-ordered the variables in a correlation matrix and displayed the value by sign and magnitude. All iconic encodings in the matrix displayed the pattern and significance level of correlations between variables. The R package "corrgram" and "Hmisc" were employed in this study.

ML algorithms.
Based on the R Programming Language (R Core Team, Vienna, Austria), four ML models, including SVM, ANN, LR model and RF, were constructed. The dataset was randomly split into two mutually exclusive sets, training (70%) and testing (30%), a method called holdout method 29 . LR model established with variable choice through backward elimination was implemented to assess risk factors and predict the diagnosis of diseases. The R package "e1071" was applied in the SVM model to accomplish regression and classification missions by constructing hyperplanes in a multidimensional space. SVM model could manage multiple continuous and categorical variables according to the decision plane. ANN model, a computerized encoding of artificial humanoid neuronal networks, included the input layer, hidden layers, and output layer. Neurons connected the adjacent layers as a medium for the delivery-feedback-correction-delivery cycle. This recursive process adjusted the weights for fewer errors and better accuracy. ANN model was implemented by R package "neural net". RF model, a ML algorithm based on the decision tree, could combine the output of a single decision tree to improve the overall performance. RF model was superior to a single decision tree in eliminating overfitting. RF model also could display the relative importance of the variables by the Gini index. We utilized the R package "random-Forest" in the establishment of the RF model.

Statistical analysis.
The chi-square test and Fisher's exact test were applied to compare the variables of severe MBL cases and normal controls. We utilized the Cochran-Armitage trend test for categorical variables, while continuous variables were assessed by Student's t-test and the Mann-Whitney rank-sum test. R programming language was used for all statistical analyses, while P < 0.05 was regarded as statistically significant.

Data availability
All CBCT files of patients and control subjects were stored in a non-public medical record database. CBCT data of the samples will not be shared. License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.