Numerical modelling of the deformation of elastic material by the TLM method

The transmission line matrix (TLM) method is a numerical tool for the solution of wave and diffusion type equations. The application of TLM to physical phenomena such as heat flow and electromagnetic wave propagation is well established. A previous attempt to apply TLM models to the area of elastic wave propagation and elastic deformation had limited success. The work of this thesis extends the application base of TLM to the area of elastic deformation modelling and validates the model for several two-dimensional situations. In doing this it has been necessary to develop new nodal structures which facilitate the scaling of differential coefficients and incorporation of cross derivatives. Nodal structures which allow the modelling of two and three-dimensional, and anisotropic, elastic deformation are described.The technique is demonstrated by applying the elastic deformation model to several elastic problems. These include two-dimensional isotropic models and models of anisotropic elastic deformation. Provision is also made for the application of various boundary conditions which include displacement, force and frictional boundaries

Biomechanical Soft Tissue Modeling - Techniques, Implementation and Application

The reaction of soft tissue to applied forces can be calculated with biomechanical simulation algorithms. Several modeling approaches exist. A scheme is suggested which allows the classification of arbitrary modeling approaches with respect to the degree of physical realism contained in the model (physical and descriptive models). Besides well known approaches like mass-spring, finite element, particle models and others the ChainMail algorithm is investigated. Where ChainMail in its original formulation lacked the capability to model inhomogeneous material, it is exceptionally stable and converges in one step to a valid configuration. In this thesis ChainMail is generalized to the Enhanced ChainMail algorithm which is capable to model inhomogeneous, volumetric objects and is fast enough for real time simulations. While now in principle being able to simulate and visualize an object in real time, a software architecture is required to team up simulation and visualization. As visualization and simulation have so far evolved independently, they work with different data structures. Multiplicity of data representations leads to the problems of data consistency and high memory consumption. A software architecture is developed which provides a universal data structure for several simulation and visualization approaches. The versatility of the developed architecture is demonstrated by two medical simulations. The first is the simulation of an intra-ocular surgery, which makes heavy use of Virtual Reality techniques. Designed as a training and educational tool the simulator EyeSi relies on descriptive real time ti me tissue simulation and visualization. The second deals with the simulation of decompressive craniotomy. The medical problem requires a physical model as the project's goal is to provide exact predictions on tissue behavior to support surgeons in surgery planning