This study aims to develop a high-precision predictive model for grinding forces generated by ultrasonic bone scalpels during spinal surgery, to enhance safety by establishing quantitative operational boundaries. Existing predictive models often rely on simplified 2D simulations or theoretical decompositions, which may limit accuracy in capturing the complex three-dimensional kinematics and tool-bone interactions. To address this, an integrated framework combining three-dimensional explicit dynamic finite element analysis (FEA) with a Box-Behnken experimental design and response surface methodology was developed. The FEA model realistically simulates tool-bone interaction, while the RSM systematically investigates the coupling effects of bone density (480-800-1640 kg/m3), ultrasonic amplitude (60-100 μm), and feed rate (1-4 mm/s). A second-order polynomial model was derived, revealing that the grinding force increased with bone density (coefficient: + 3.10) and feed rate (coefficient: + 2.55), but decreased with ultrasonic amplitude (coefficient: - 2.52). Rigorous validation via analysis of variance residual diagnostics, and robotic-assisted physical experiments confirmed a maximum prediction error of 7.10%, demonstrating higher accuracy than existing models. Based on a 20 N safety threshold, clinically actionable safety boundaries were visualized as heatmaps, offering clear guidance for parameter selection. This work provides a validated computational-experimental framework that supports data-driven surgical planning and lays a foundation for intelligent, force-feedback robotic systems in spinal surgery, enhancing both safety and precision.
Li et al. (Mon,) studied this question.