Data structures have been explored for several domains of computer applications in order to ensure efficiency in the data store and retrieval. However, data structures can present different behavior depending on applications that they are being used. Three-dimensional interactive environments offered by techniques of Virtual Reality require operations of loading and manipulating objects in real time, where realism and response time are two important requirements. Efficient representation of geometrical models plays an important part so that the simulation may become real. In this paper, we present the implementation and the comparison of two topologically efficient data structures-Compact Half-Edge and Mate Face -for the representation of objects for three-dimensional interactive environments. The structures have been tested at different conditions of processors and RAM memories. The results show that both these structures can be used in an efficient manner. Mate-Face structure has shown itself to be more efficient for the manipulation of neighborhood relationships and the Compact Half-Edge was more efficient for loading of the geometric models. We also evaluated the data structures embedded in applications of biopsy simulation using virtual reality, considering a deformation simulation method applied in virtual human organs. The results showed that their use allows the building of applications considering objects with high resolutions (number of vertices), without significant impact in the time spent in the simulation. Therefore, their use contributes for the construction of more realistic simulators. (C) 2016 Elsevier Inc. All rights reserved.