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

Rohit Kaushik, Eva Kaushik

TL;DR

A unified framework that combines nonlinear dynamics, perceptual psychophysics and high frequency haptic rendering to enhance realism in surgical simulation and discusses 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.

Abstract

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.

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

TL;DR

A unified framework that combines nonlinear dynamics, perceptual psychophysics and high frequency haptic rendering to enhance realism in surgical simulation and discusses 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.

Abstract

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.
Paper Structure (64 sections, 1 theorem, 39 equations, 5 figures, 2 tables)

This paper contains 64 sections, 1 theorem, 39 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Haptic Fidelity in Surgical Simulators
  4. Energy-based Rendering Approaches
  5. Perceptual Realism Studies
  6. Deformable Modeling for Haptics
  7. Multi-modal Force Sensing in Surgical Tools
  8. Gaps
  9. Modeling Framework and Methodology
  10. Nonlinear Dynamics and Koopman Embedding
  11. Force Computation Module
  12. Latency Modeling and Compensation
  13. Bayesian Perceptual Scaling
  14. Perceptual Calibration via Bayesian Psychophysics
  15. Hierarchical Psycho-physical Scaling
  16. ...and 49 more sections

Key Result

Theorem 1

Assume $f$ is Lipschitz continuous and inputs $u(t)$ are bounded. Then the EDMD-learned Koopman operator $K$ satisfies:

Figures (5)

  • Figure 1: Improvement in perceptual discrimination across tasks. Bars indicate mean accuracy; error bars represent 95% confidence intervals from Bayesian posterior samples.
  • Figure 3: Dental Surgery Simulation
  • Figure 4: Koopman lifting from nonlinear tissue dynamics to a linear space for predictive haptic rendering.
  • Figure 5: Voxel-based collision detection and proxy force computation for micro-resolution organ models.
  • Figure 6: Bayesian perceptual calibration pipeline for mapping simulated forces to human JND thresholds.

Theorems & Definitions (1)

  • Theorem 1: Bounded Koopman Prediction Error