Implicit models inherently support automatic blending and trivial collision detection which makes them an effective tool for designing complex organic shapes with many applications in various areas of research including surgical simulation systems. However, slow rendering speeds can adversely affect the performance of simulation and modelling systems. In addition, when the models are incorporated in a surgical simulation system, interactive and smooth cutting becomes a required feature for many procedures. In this research, we propose a comprehensive framework for high-performance rendering and physically-based animation of tissues modelled using implicit surfaces. Our goal is to address performance and scalability issues that arise in rendering complex implicit models as well as in dynamic interactions between surgical tool and models. Complex models can be created with implicit primitives, blending operators, affine transformations, deformations and constructive solid geometry in a design environment that organizes all these in a scene graph data structure called the BlobTree. We show that the BlobTree modelling approach provides a very compact data structure which supports the requirements above, as well as incremental changes and trivial collision detection. A GPU-assisted surface extraction algorithm is proposed to support interactive modelling of complex BlobTree models. Using a finite element approach we discretize those models for accurate physically-based animation. Our system provides an interactive cutting ability using smooth intersection surfaces. We show an application of our system in a human skull craniotomy simulation. / Graduate / 0984 / pourya.shirazian@gmail.com