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