A method of modeling anatomic deformation comprises receiving a reference three dimensional model of a branched anatomical formation in a reference state. The method further comprises detecting deflection of the branched anatomical fomation with a shape sensor to create a three dimensional deformation field. The method further comprises applying the three dimensional deformation field to the reference three dimensional model to create a deformed three dimensional model of a deformed state of the branched anatomical formation. The method further comprises dynamically displaying an image of the deformed three dimensional model of the deformed state of the branched anatomical formation. The method further comprises displaying a composite image including an image of an interventional instrument positioned within the branched anatomical formation and the dynamically displayed image of the deformed three dimensional model of the deformed state of the branched anatomical formation.