A Koopman-Bayesian Framework for High-Fidelity, Perceptually Optimized Haptic Surgical Simulation

We introduce a unified framework that combines nonlinear dynamics, perceptual psychophysics and high frequency haptic rendering to enhance realism in surgical simulation. The interaction of the surgical device with soft tissue is elevated to an augmented state space with a Koopman operator formulation, allowing linear prediction and control of the dynamics that are nonlinear by nature. To make the rendered forces consistent with human perceptual limits, we put forward a Bayesian calibration module based on WeberFechner and Stevens scaling laws, which progressively shape force signals relative to each individual's discrimination thresholds. For various simulated surgical tasks such as palpation, incision, and bone milling, the proposed system attains an average rendering latency of 4.3 ms, a force error of less than 2.8% and a 20% improvement in perceptual discrimination. Multivariate statistical analyses (MANOVA and regression) reveal that the system's performance is significantly better than that of conventional spring-damper and energy, based rendering methods. We end by discussing the potential impact on surgical training and VR, based medical education, as well as sketching future work toward closed, loop neural feedback in haptic interfaces.