Interactive Physical Simulation of Catheter Motion within Mayor Vessel Structures and Cavities for ASD/VSD Treatment

摘要

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.