Physics-Informed Generative Framework to Unsupervised Biomechanical Parameter Estimation for Tool–Tissue Force Prediction from Laparoscopic Depth Maps

Physically consistent estimation of soft-tissue mechanical properties is critical for surgical robotics, intraoperative safety monitoring, and simulator initialization, yet existing methods typically require force-sensing hardware or manual parameter tuning. This paper presents a physics-informed generative framework that estimates tissue stiffness (ks), damping coefficient (kd), and tool–tissue contact force magnitude (Fmag) from monocular laparoscopic video in a label-free manner with respect to mechanical parameters and interaction forces. The pipeline integrates three components: DepthPro, a multi-scale Vision Transformer (ViT) for zero-shot metric depth estimation; a 3D geometric contact detection pipeline; and a dual-mode conditional generative network trained via a five-term physics–adversarial loss. A differentiable Mass–Spring–Damper (MSD) simulator is embedded directly in the training loop. This enables gradient-based parameter learning without force-sensor, displacement, or boundary-condition supervision. Parameter identifiability is supported through dual observational grounding: MSD physics consistency against observed contact displacement, and next-frame depth map reconstruction. Validated on CholecSeg8k cholecystectomy sequences, Physics-Informed Neural Network (PINN)-estimated parameters significantly outperform static literature baselines (Wilcoxon p = 2.49 × 10−8, Cohen’s d = 0.374), with physically plausible viscoelastic settling dynamics recovered within 0.9 s of tool release. Since no force sensors were present at acquisition time, evaluation follows an indirect simulation-consistency protocol. Mechanical parameters are estimated at 1.6 ms/frame, a negligible addition to the monocular depth front end that sets the pipeline rate. Estimated parameters directly enable stiffness-aware haptic rendering, intraoperative safety monitoring, and scene-adapted surgical simulation initialization.