This paper presents a technique for the segmentation of anatomic structures in medical images using a topologically adaptable snakes model. The model is set in the framework of domain subdivision using simplicial decomposition. This framework allows the model to maintain all of the strengths associated with traditional snakes while overcoming many of their limitations. The model can ow into complex shapes, even shapes with signi cant protrusions or branches, and topological changes are easily sensed and handled. Multiple instances of the model can be dynamically created, can seamlessly split or merge, or can simply and quickly detect and avoid collisions. Finally, the model can be easily and dynamically converted to and from the traditional parametric snakes model representation. We apply a 2D model to segment structures from medical images with complex shapes and topologies, such as arterial \trees", that cannot easily be segmented with traditional deformable models.