Machine Learning Surrogate Modeling for Finite-Element Biomechanical Prediction and Design Screening in Implant-Supported Prostheses

Finite-element analysis (FEA) is a widely used computational method for predicting the biomechanical response of implant-supported prostheses, but its computational cost limits its use in large-scale parametric exploration or chairside decision support. This study evaluated whether supervised machine learning models trained on finite-element simulations can act as accurate, near-instantaneous surrogates, whether their predictions are driven by physically plausible input variables, and whether their residual error is small enough to preserve the verdict of a downstream, illustrative design-screening protocol. A finite-element dataset was generated for 100 independently meshed and solved parent configurations of a fixed, four-implant (“All-on-4”-type) implant-supported prosthesis, varying seven geometry-level input variables (bone quality, bar material, implant diameter and length, implant tilt angle, cantilever length, and occlusal load angle) using a custom three-dimensional finite-element solver implemented in Python; each parent solution was then linearly scaled to 71 occlusal-load magnitudes, yielding a 7100-row modeling dataset with four biomechanical outputs per row: 95th-percentile (P95) cortical bone von Mises stress, P95 trabecular bone von Mises stress, maximum prosthesis displacement, and P95 bone principal strain. All 100 parent simulations converged and passed internal quality-control checks on solver residuals and force-balance equilibrium. Because rows sharing a parent geometry are not statistically independent, all partitioning and cross-validation were performed at the geometry level: 20 geometries (1420 rows) were held out a priori as a fixed test set, and the remaining 80 geometries (5680 rows) formed a development pool on which Random Forest, XGBoost, and support-vector regression (SVR) models were compared using grouped cross-validation GroupKFold keyed on parent geometry, 5 folds × 5 repeats, 25 matched folds), with model selection performed independently for each output based on the lowest mean cross-validated RMSE. This yielded a different winning model per output rather than a single globally best algorithm: target-scaled SVR for both P95 cortical stress (1.919±0.501 MPa) and P95 trabecular stress (0.168±0.039 MPa), Random Forest for maximum displacement (0.190±0.079 mm), and XGBoost for P95 principal strain (166.3±77.8 με). Friedman and Holm-corrected pairwise Wilcoxon signed-rank tests corroborated that this ranking was consistent across resampled folds, but the more practically relevant evidence is the magnitude of the differences themselves, which is reported primarily as percentage RMSE reduction and matched-pairs rank-biserial effect size: 14.5% (cortical stress), 1.5% (trabecular stress, a practically negligible difference), 9.4% (displacement), and 15.0% (principal strain). Each selected model was refit on the full 80-geometry development pool and evaluated once, without further tuning, on the fixed 20-geometry (1420-row) test set. On this held-out test set, the selected models achieved coefficients of determination (R2) of 0.985 (95% bootstrap CI 0.976 to 0.993) for cortical stress, 0.968 (0.946 to 0.982) for trabecular stress, 0.986 (0.977 to 0.993) for maximum displacement, and 0.931 (0.883 to 0.980) for principal strain, with mean absolute percentage errors between 7.99% and 14.88%. SHAP (SHapley Additive exPlanations) analysis of the actual selected model for each output (TreeExplainer for Random Forest and XGBoost; KernelExplainer for SVR) showed that occlusal load magnitude was the dominant driver of both stress outputs and of principal strain (39 to 45% of attributed importance), bone quality contributed materially to trabecular stress and strain (19% and 31%, respectively), and bar material was the leading driver of maximum displacement (50%), whereas implant diameter and tilt angle together contributed well under 10% of attributed importance for every output. Applying an illustrative biomechanical design-screening protocol (combining Frost’s mechanostat strain zones with Misch bone-quality-adjusted safety margins, with structural veto thresholds calibrated on the 80-geometry development pool only) independently to the true and surrogate-predicted outputs of all 1420 held-out test rows yielded an identical screening flag in 1301 rows (91.6%), with discordant rows concentrated close to a decision-zone boundary (89.9% of discordances within 20% of the boundary) rather than distributed uniformly across the design space, and this agreement rate was stable (91.5 to 92.3%) across alternative Misch discount-factor magnitudes. These results indicate that, within the sampled design space of this parametric finite-element model, output-specific machine learning surrogates can reproduce its biomechanical outputs with good numerical accuracy and physically interpretable feature attributions at a fraction of the computational cost, supporting their exploratory use as surrogate models for rapid design screening rather than as a substitute for clinical judgment or experimental validation.