The modelling of interactions between organs and medical tools: a volumetric mass-spring chain algorithm

This paper adds volume deformation capability to the mass-spring chain method using tetrahedral elements in order to obtain more realistic deformations, which occur during the interactions between medical tools and soft tissues. The mass-spring chain method originally does not consider volume information and performs deformation by moving and deforming individual springs of a deformable model. However, most of the applications in computer graphics require volume modelling using tetrahedrons. In the proposed method, the deformation algorithm loops through tetrahedrons and performs deformation based on defined rules similar to those of the original mass-spring chain method. This method can handle not only ordinary deformation applications but also those with topology changes, such as cutting and tearing, as it does not rely on any pre-computed quantities. A method to preserve the volume and the shape of the tetrahedral elements is also developed. In order to speed up the new version of the algorithm, a tetrahedral propagation for deformation is developed. The detailed implementation of the algorithm and the various applications of the organ-surgery tool interactions are presented. The paper also provides the animations of the different models obtained by the proposed method.