Modeling Torsion of Blood Vessels in Surgical Simulation and Planning

This paper proposes a hybrid approach for modeling torsion of blood vessels that undergo deformation and joining. The proposed model takes 3D mesh of the blood vessel as input. It first fits a generalized cylinder to extract the blood vessel's medial axis. Then, it uses rotation minimizing frame as a reference to model and measure the torsion of blood vessel after deformation. In general, the proposed approach can incorporate any kind of deformation algorithms. In our experiments, differential geometry method is used as an example. The test results show that our algorithm can correctly and effectively evaluate the amount of torsion caused by blood vessel deformation. In addition, it can also determine the configuration of the blood vessel with minimum torsion.