Fig 1. The physical properties of coils and how they were modeled.

Top Row: The coil’s primary stock wire is composed of platinum and was not modeled in either technique. 2nd Row: The coil’s secondary structure comprises the stock wire wound to form a helical spring-like structure. The secondary structure was modeled as a series of beam elements in both techniques, with the Improved Technique using hollow elements and the Original using solid elements. 3rd Row: The coils tertiary “pre-shape” is created when the spring-like structure is wound around a mandrel and heat-treated to create a 3D shape with “shape-memory”. The Original Technique modeled the pre-shape as mathematical curves generated from parametric equations, while the Improved Technique modeled the pre-shape by virtually winding the coil’s secondary structure around a mandrel. Bottom Row: We modeled coil mechanical properties after springs, with the Original Technique assuming beam elements had the elastic moduli of a platinum wire and the Improved Technique calculating beam properties by equating beam rigidity to spring rigidity.