A system to characterize motion of an anatomical structure (114, 402, 502), comprising: a sensor (106, 208, 406, 516, 604, 702) attached to an apparatus (400, 500, 600, 700), which is configured for insertion within the anatomical structure; a tracking system (110, 204, 1202) that generates tracking data representing at least a position of the sensor in a three-dimensional tracking coordinate system over time; and a computing device (112, 1200) that includes a processor to execute machine-readable instructions, the instructions to at least: compute a motion model characterizing a behavior of the anatomical structure over a time interval based on at least one free parameter and a temporal parameter, the free parameter estimating geometry of the anatomical structure derived from the tracking data, and the temporal parameter indexing the free parameter over the time interval; and generate a graphical representation of the motion model to visualize the behavior of the anatomical structure over the time interval; characterized in that the apparatus comprises an elongate guidewire (102, 404, 608, 708) and at least one set of mechanically biased legs (412, 512, 606, 706); wherein the at least one set of mechanically biased legs (412, 512, 606, 706) extend outwardly from a first end thereof that is attached to the guidewire and terminate in distal ends (416, 514) of the at least one set of mechanically biased legs, each set of legs being mechanically biased to retain the guidewire at a central location between the distal ends thereof when engaging contact locations along an interior wall of the anatomical structure (114, 402, 502). a sensor (106, 208, 406, 516, 604, 702) attached to an apparatus (400, 500, 600, 700), which is configured for insertion within the anatomical structure; a tracking system (110, 204, 1202) that generates tracking data representing at least a position of the sensor in a three-dimensional tracking coordinate system over time; and a computing device (112, 1200) that includes a processor to execute machine-readable instructions, the instructions to at least: compute a motion model characterizing a behavior of the anatomical structure over a time interval based on at least one free parameter and a temporal parameter, the free parameter estimating geometry of the anatomical structure derived from the tracking data, and the temporal parameter indexing the free parameter over the time interval; and generate a graphical representation of the motion model to visualize the behavior of the anatomical structure over the time interval; characterized in that compute a motion model characterizing a behavior of the anatomical structure over a time interval based on at least one free parameter and a temporal parameter, the free parameter estimating geometry of the anatomical structure derived from the tracking data, and the temporal parameter indexing the free parameter over the time interval; and generate a graphical representation of the motion model to visualize the behavior of the anatomical structure over the time interval; the apparatus comprises an elongate guidewire (102, 404, 608, 708) and at least one set of mechanically biased legs (412, 512, 606, 706); wherein the at least one set of mechanically biased legs (412, 512, 606, 706) extend outwardly from a first end thereof that is attached to the guidewire and terminate in distal ends (416, 514) of the at least one set of mechanically biased legs, each set of legs being mechanically biased to retain the guidewire at a central location between the distal ends thereof when engaging contact locations along an interior wall of the anatomical structure (114, 402, 502).