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This paper presents an approach to performing time-critical collision detection for deformable objects. The deformable objects are represented by dense meshes and their deformations are steered by a coarser mesh (reduced model) based on explicit finite elements, to achieve an interruptible algorithm, we use a sphere tree constructed using an adaptive medial-axis approximation of the dense mesh. The bounding spheres are updated using the coarse mesh, thus balancing computational accuracy and speed.