Haptic Interaction with Segmented Medical Image Embedded in Finite Element Mesh

Abstract

Progress in haptic technology has enabled the development of surgery simulators with haptic feedback, and the simulators are expected to help surgeons train in various surgical procedures in an efficient way 1). In the simulators, a finite element（FE）mesh, typically a tetrahedral or hexahedral mesh, is required for the mechanical analysis of biological tissues using the finite element method（FEM). Although current meshing software generates good-quality volumetric meshes for simple geometries, mesh generation of a highly irregular geometry such as the brain is still difficult 2). Even if the mesh generation succeeds, the resulting mesh is not always appropriate for real-time simulation；i.e., too fine a mesh cannot be used in real-time finite element analysis（FEA）owing to its high computational cost. Although a mesh can be generated with a large mesh size to obtain a reasonable computational cost, it is difficult to preserve the fine features in a coarse mesh for complex organs. This fact make it inefficient to construct a virtual environment for surgical training or to generate a patient-specific model for preoperative planning. One of the effective approaches for the mesh generation of complex objects is embedding. In the computer graphics community, a fine geometry（typically a polygonal surface） is often embedded in a coarse volumetric mesh 3),4). In most cases, a coarse volumetric mesh is a regular structured grid that covers all the primitives in a fine geometry, and thus mesh generation is simple, fast, and robust. The deformation of a fine geometry is interpolated with that of a coarse volumetric mesh in a master-slave manner. This enables separation of the model for graphics rendering and for mechanical analysis. As a result, good visual plausibility and a reasonable computational cost are achieved at the same time. The embedding technique is not limited to applications for polygonal surfaces but can also be applied to volume data such as medical images. We Kazuya Sase／ 89 • Abstract The generation of patient-specific models is one of the difficult problems in the clinical application of surgery simulators. In particular, when estimation of soft tissue deformation is required, a finite element（FE）mesh needs to be generated from the patientʼs medical images. One of the effective methods of FE mesh generation is the volume embedding approach. In this approach, the medical volume data are embedded in a simple volumetric mesh such as orthogonal grid. However, the volume embedding method generates an incorrect boundary surface in the FE mesh. This makes it difficult to solve the contact problem between tools and embedded volumes. In this paper, an efficient contact handling method for embedded volumes using the signed distance field is described. In addition, its application to haptic rendering is introduced.