Systems and method for determining the shape of a surgical instrument and surgical instruments having a deformable body

A surgical instrument comprising:

• an elongate flexible body;
• tracking sensor disposed at a tip of the deformable body, the tracking sensor determining a measured spatial position and orientation of the tip of the elongate flexible body;
• and
• a physical parameter sensor operatively coupled with the elongate flexible body, the physical parameter sensor determining at least one parameter of the elongate flexible body of the surgical instrument,
• wherein the spatial position and/or shape of the elongate flexible body is determinable using a predefined elasticity model of the elongate flexible body, wherein the predefined elasticity model describes deformation of the elongate flexible body of the surgical instrument as a function of:
• the measured spatial position and orientation of the tip of the elongated deformable body;
• and
• an influence on the elongate flexible body of the surgical instrument by the at least one parameter of the elongate flexible body of the surgical instrument.

A system comprising:

• a surgical instrument comprising an elongate flexible body;
• a tracking sensor disposed at a tip of the elongate flexible body, the tracking sensor determining a measured spatial position and orientation of the tip of the elongate flexible body;
• a physical parameter sensor operatively coupled with the elongate flexible body, the physical parameter sensor determining at least one parameter of the elongate flexible body of the surgical instrument;
• a processor;
• a memory device operatively coupled with the processor;
• a predefined elasticity model of the elongate flexible body stored in the memory device, wherein the predefined elasticity model describes deformation of the elongate flexible body of the associated surgical instrument as a function of:
• a spatial position and orientation of a tip of the elongate flexible body of the associated surgical instrument;
• and
• an influence on the elongate flexible body of the associated surgical instrument by at least one parameter;
• and
• logic stored in the memory device, the logic being executable by the processor to calculate the spatial position and the shape of an elongate flexible body of an associated surgical instrument based on applying:
• i) the at least one parameter determined by the physical parameter sensor;
• and ii) the measured spatial position and orientation of the tip of the elongate flexible body determined by the tracking sensor to the predefined elasticity model of the elongate flexible body in the memory device.