An analytic meshless enrichment function for handling discontinuities in interactive surgical simulation

For surgical simulation applications, realistic behavioral modeling of soft tissue is considered to be one of the most significant challenges, because biomechanical soft-tissue models need to reflect the correct elastic response, be efficient in order to run at interactive simulation rates, and be able to support operations such as cuts and sutures. For these reasons, having a usable 3D cutting engine is a significant feature for interactive surgery simulation software. Mesh-based solutions, where the connections between the individual degrees of freedom (DoF) are defined explicitly, have been the traditional approach to soft-tissue biomechanics. However, when the problem under investigation in interactive biomechanics contains a simulated surgical gesture that entails a cut that disrupts the connectivity, the underlying mesh structure has to undergo remeshing operation, and most of the time it causes the performance bottleneck in the simulation. Unlike the tightly-coupled nonoverlapping element composition of the mesh-based solutions, this paper builds an analytic enrichment function on top of a loosely-coupled meshless method for constitutive modeling of elastic soft tissues, where arbitrary discontinuities or cuts are applied to the objects in the context of surgical simulation. Enrichment values for a continuous cut interface are computed and stored inside a grid structure that is accessed by individual meshless nodes in order to update their weight functions. The presented analytic enrichment function is efficient to compute and easy to integrate into existing meshless models. The meshless mechanics code and the enrichment-based cut handling functionalities have been implemented within the open-source simulation framework SOFA.