A non-transitory machine-readable media stores instructions that, when run by one or more processors, cause the one or more processors to store a deformable model of a patient anatomy and deform the deformable model based on a measured deformation of a branched anatomical structure of the patient anatomy. The deformable model includes a skeleton tree of nodes and linkages representing the branched anatomical structure of the patient anatomy. Each of the nodes is located at a respective bifurcation of the branched anatomical structure, and at each respective bifurcation the corresponding linkages include an orientation. The deformable model is deformed by modifying the orientations of the linkages of the branched anatomical structure.