Adaptive surface representation based on homogeneous hexahedrons for interactive simulation of soft tissue cutting

Interactive simulation of cutting soft tissues is essential in simulation of surgery and medical procedures. Cutting simulation involves topological and geometrical changes of the finite elements, and requires significant additional computational burden. This problem is handled, in this paper, by approximating a small gap between the model boundaries and the volumetric finite elements.

Deformations are computed using only the regular hexahedrons, and the surface structure is embedded in the hexahedrons for visualizing the objects and detecting the collisions. Cutting is handled separately for the hexahedrons and the surface structure. The intersected hexahedrons are duplicated in the cutting without geometrical changes, and the surface structure is conformed to the cutting path to represent the cut surfaces faithfully. A method of using partial elements is introduced to compensate for inaccuracies due to the gap between the cut surface and the hexahedron.

Simulation results show that the additional computation burden of the proposed method is reduced to 34% and 37.12% of the previous method in the literature. The theoretical range of additional arithmetic operations for each method is derived, showing the superiority of the proposed method.

The proposed method improves the real-time performance of the simulation through an adaptive approximation of the cut surface.