A novel deformation method for fast simulation of biological tissue formed by fibers and fluid

This paper presents a new approach to the simulation of soft tissues deformation suitable for real time computation, particularly intriguing for medical applications. The approach implements a quasi-static solution for elastic global deformations of objects filled with fluid and fibers, which can be a good approximation for biological tissues. It is based on the Pascal's principle and the conservation of volume. Large deformations that quickly change the whole shape of the object can be stably simulated in a small number of time steps. In our approach each pair of surface vertices is connected and defines an elastic fiber. The set of all the elastic fibers defines a mesh of an order of magnitude smaller than the volumetric meshes, allowing the simulation of complex objects with less computational effort. The proposed method was applied to study the effects of forces for deformation and displacement of soft geometrical objects (rod, sphere, etc.) in order to analyze the results on simple forms. Then a compression similar to the deformation obtained during a mammographic examination procedure is applied to a breast. A preliminary validation is done by comparing deformation result between our new method and real ex vivo bovine liver. The results of this comparison show a high degree of similarities between the experimental results and deformations calculated by our method. This new method is suited to isotropic or anisotropic elasticity and linear or nonlinear stress-strain relationship. Finally, the results of the deformations were shown to be independent of the mesh discretization for our method.