Surgical simulators provide another tool for training and practising surgical procedures, usually restricted to the use of cadavers. Our surgical simulator utilises Finite Element (FE) models based on linear elasticity. It is driven by displacements, as opposed to forces, allowing for realistic simulation of both deformation and haptic response at real-time rates. To achieve demanding computational requirements, the stiffness matrix K, which encompasses the geometrical and physical properties of the object, is precomputed, along with K⁻¹. Common to many surgical procedures is the requirement of cutting tissue. Introducing topology modifications, such as cutting, into these precomputed schemes does however come as a challenge, as the precomputed data needs to be modified, to reflect the new topology. In particular, recomputing K⁻¹ is too costly to be performed during the simulation. Our topology modification method is based upon updating K⁻¹ rather than entirely recomputing the matrix. By integrating condensation, we improve efficiency to allow for interaction with larger models. We can further enhance this by redistributing computational load to improve the system's real-time response. We exemplify our techniques with results from our surgical simulation system.

We present an extension of our work on topology modification and deformation for Finite Element Models, in which the inverse stiffness matrix is updated rather than recomputed entirely. Previously we integrated condensation to allow for realistic interaction with larger models. We improve on this by redistributing computational load to increase the system's real-time response. Removing a tetrahedron only requires data associated with the nodes of that tetrahedron, and the surface nodes, to be updated, in order to drive the simulation. However, the update procedure itself needs the entire data structure to be updated. The equations used to update the inverse stiffness matrix are split up such that calculations are only performed for the affected nodes. Data regions corresponding to the surface nodes necessary for deformation calculations are computed immediately, whilst remaining regions can be computed as required, resulting in up to a ten-fold improvement in system response times.

Cuts on deformable organs are a central task in the set of physical operations needed in many surgical simulation environments. Our BioMedIA surgical simulator structures are Finite Element Models, driven by displacements on the touched nodes as opposed to forces. This approach allows for realistic simulation of both deformation and haptic response at real-time rates. The integration of condensation into our system increases its efficiency, and allows for complex interaction on larger meshes than would normally be permitted with available memory. We present an extension of our novel algorithm for cuts in deformable organs, in the context of condensed matrices. We show results from our surgical simulation system with real-time haptic feedback.

In this paper we present a technique for the modelling of realistic collisions between arbitrary rigid surgical tools and deformable geometry that is independent of the resolution of colliding objects. We use a spatial hash table to provide an efficient narrow-phase collision detection and modelling backend. This is combined with previous work on collision modelling in our surgical simulation environment to model realistic collisions and collision response at haptic rates.

We present a novel method of contact modelling for discrete deformable models. Our algorithm is used to simulate contact between rigid surgical tools of arbitrary shape and deformable virtual organs bounded by triangular mesh surfaces. It uses a divide and conquer strategy to redistribute an arbitrary field of displacements on organ surfaces into an equivalent field of displacements at the nodes. The computational complexity depends on the size of the touch field, but not on the size of the mesh representing the organ. Our algorithm results in accurate modelling and can be used in real-time applications requiring haptic feedback.