Active contour models have already been used succesfully for segmentation of organs from medical images in 3D. In implicit models, the contour is given as the isosurface of a scalar function, and therefore topology adaptations are handled naturally during a contour evolution. Nevertheless, explicit or parametric models are often preferred since user interaction and special geometric constraints are usually easier to incorporate. Although many researchers have studied topology adaptation algorithms in explicit mesh evolutions, no stable algorithm is known for interactive applications. In this paper, we present a topology adaptation system, which consists of two novel ingredients: A spatial hashing technique is used to detect self-colliding triangles of the mesh whose expected running time is linear with respect to the number of mesh vertices. For the topology change procedure, we have developed formulas by homology theory. During a contour evolution, we just have to choose between a few possible mesh retriangulations by local triangle-triangle intersection tests. Our algorithm has several advantages compared to existing ones: Since the new algorithm does not require any global mesh reparametrizations, it is very efficient. Since the topology adaptation system does not require constant sampling density of the mesh vertices nor especially smooth meshes, mesh evolution steps can be performed in a stable way with a rather coarse mesh. We apply our algorithm to 3D ultrasonic data, showing that accurate segmentation is obtained in some seconds.