Passivity-Preserving Smoothing of Force Discontinuities at Tissue Boundaries in Haptic Surgical Simulation

Haptic surgical simulators assign a constitutive force law to each tissue class segmented from volumetric images and switch between laws, unsmoothed, as the instrument advances. This study characterizes the resulting force discontinuities and derives energy-consistent remedies. The artifacts were quantified on a layered brain-tissue model and on the standard needle-insertion formulation, classified by the variable that triggers the switch, and treated by position-domain blending with a closed-form, velocity-adaptive transition width and by a continuous velocity-domain friction law. Unsmoothed force steps reach 8.6 times the quasi-static force-discrimination threshold reported in the literature and exceed it across 95% of the needle model’s parameter space. Blending reduces the peak rendered jerk by more than an order of magnitude at a boundary blur below the imaging voxel size and leaves the force field conservative, preserving passivity by construction, whereas a first-order low-pass filter applied to the rendered force can violate passivity under the conditions considered, injecting energy in proportion to its time constant. Switching artifacts are therefore fidelity rather than stability defects and can be removed at negligible cost by smoothing in the domain of the switching variable. These perceptual comparisons are numerical and await validation with human participants.