Simulation systems are becoming increasingly essential in medical education. Hereby, capturing the physical
behaviour of the real world requires a sophisticated modelling of instruments within the virtual environment.
Most models currently used are not capable of user interactive simulations due to the computation of the
complex underlying analytical equations. Alternatives are often based on simplifying mass-spring systems, being
able to deliver high update rates that come at the cost of less realistic motion. In addition, most techniques
are limited to narrow and tubular vessel structures or restrict shape alterations to two degrees of freedom, not
allowing instrument deformations like torsion.
In contrast, our approach combines high update rates with highly realistic motion and can in addition be used
with respect to arbitrary structures like vessels or cavities (e.g. atrium, ventricle) without limiting the degrees of
freedom. Based on energy minimization, bending energies and vessel structures are considered as linear elastic
elements; energies are evaluated at regularly spaced points on the instrument, while the distance of the points is
fixed, i.e. we simulate an articulated structure of joints with fixed connections between them. Arbitrary tissue structures are modeled through adaptive distance fields and are connected by nodes via an
undirected graph system. The instrument points are linked to nodes by a system of rules. Energy minimization
uses a Quasi Newton method without preconditioning and, hereby, gradients are estimated using a combination
of analytical and numerical terms.
Results show a high quality in motion simulation when compared to a phantom model. The approach is also
robust and fast. Simulating an instrument with 100 joints runs at 100 Hz on a 3 GHz PC.