Topological Model with Adaptive Resolution to Simulate an Incision in Surgery

Abstract

Surgical simulation covers a set of very large fields. Medical physics simulation, which aims to virtually reproduce the behavior of organic tissues, tries to stick, as far as possible, with reality. This last field poses many concrete problems currently very incompletely resolved, and the extreme mechanical complexity of living tissues. The mechanical interaction between organs, the large number of different tissues and topologies, make the physical simulation of a human organism totally utopian at the present time. The best scientific results for the moment manage to simulate this or that type of organ, with, in terms of interaction, certain simple operations, such as primitive cutting of organs. These organs are modeled by meshes whose resolution depends on the cutting zone: the mesh associated with this zone must be defined at several scales to extract all or part of the organ considered. In addition, taking into account any cuts previously made in the vicinity of the zone considered remains an open problem that needs to be resolved. It leads to modifications of the topological model associated with the mesh. Our study therefore focuses on the adaptive resolution subdivision of triangles and tetrahedra in a mesh. Operations must preserve mesh consistency and must be robust. We propose a topology-based model that meets this need. We define and implement adaptive resolution subdivision operations in a triangular and tetrahedral mesh.