What If the External Crown Surface of Teeth Could Predict the Pulp Chamber? A DeepSDF-Based Approach

Spatial localisation of the pulp chamber is critical for safe and effective dental treatments. This study aimed to assess the performances of DeepSDF models to predict the 3D pulp chamber space and cervical line of molars using only external crown surfaces.

A fully connected auto-decoder DeepSDF network was trained on μCT-derived 3D tooth-models collected across three centres (n = 265) to learn a joint latent representation of the external and internal anatomy. Model evaluation was performed on a validation dataset from an independent external centre (n = 10). Only the external crown surface was provided to reconstruct the pulp chamber. The models were subsequently applied to clinical intraoral scans (IOS) and evaluated against corresponding cone-beam CT (CBCT) references (n = 39). Reconstruction accuracy was quantified using average surface distance, Hausdorff distance, and volumetric overlap metrics.

On μCT-derived models, the best performing DeepSDF-model reconstructed the pulp chamber with a mean surface distance of 0.18 ± 0.04 mm and a Hausdorff distance of 1.75 ± 0.21 mm, with a median of 95.9% [87.2-97.8] of surface vertices per tooth within 1 mm distance to the ground truth. The largest deviations corresponded to areas of the pulp horns (1.2 ± 0.58 mm). On clinical IOS data, predicted external surfaces showed a median distance error of 0.21 mm [0.18-0.23] and maximum distance error of 1.21 mm [1.03-1.93]. The pulp chamber was reconstructed with a median distance error of 0.49 mm [0.36-0.69], and maximum distance error of 1.49 mm [1.12-1.95]. Predicted pulp volumes were smaller, with a volumetric precision of 47% [26.5-80.7] relative to the CBCT-derived reference.

DeepSDF models learned consistent relationships between the external tooth morphology and pulp anatomy when trained and evaluated on μCT-derived data. When applied to intraoral scans, local variability was observed, particularly at the level of pulp horns. However, the overall position of the pulp chamber remained consistent. These reconstructions could be considered as an approximate representation of the internal anatomy and may provide useful support for non-invasive visualisation from intraoral scan derived surfaces and planning in digital endodontics and augmented reality-assisted procedures.