A “Point Cloud” Approach in Superelastic Stent Design

Abstract

Figure 1 shows schematically the stress-strain relation for Nitinol under uniaxial tensile test at constant temperature. Originally, material is in the Austenite phase. Upon loading, below a small strain, ε1, stress is linearly proportional to the strain. The slope defines the Young’s modulus of Nitinol in Austenite phase. When strain reaches beyond ε1, a small increase in stress induces a large amount of strain owing to the phase transition from Austenite to Martensite. After completion of the phase transition, for strain larger than ε2, the stress and strain relation is linear again with a different slope, which defines the modulus of Martensite phase. During unloading, Martensite remains until strain ε3, which is less than ε2. Below ε3, the Martensite reverts to Austenite and a large reverse strain is produced until ε4, which is smaller than ε1. After unloading below ε4, the material returns to linear elastic behavior. This unique material behavior of Nitinol, known as superelasticity, along with its excellent biocompatibility and corrosion resistance, makes Nitinol a perfect material candidate for self-expanding stent applications. Self-expanding stents made of Nitinol offer unique features such as biased stiffness to better fit the anatomy and excellent corrosion resistance. When implanted in vivo, stents are subjected to the pulsatile loading from systolic and diastolic heartbeats and therefore it is necessary to design for a long (10 years) fatigue life. Nitinol’s fatigue behavior is known to depend upon the mean and the alternating strains from cyclic loading. Therefore, one approach to ensure that the stent has a long fatigue life is to design in such a manner that both the mean and the alternating strains of the proposed stent are lower than the Nitinol’s fatigue endurance limits. For linear materials, this normally is not an issue as the location of the maximum mean strain is also the location of maximum alternating strain, therefore the history of the maximum strain point can be used to predict the device fatigue life or used as the design criterion. However, Nitinol is a highly nonlinear and path dependent material that makes it possible that the location of the maximum mean strain is not necessarily the location of maximum alternating strain. A rigorous design criterion is developed at Nitinol Devices and Components (NDC) to trace the strain history of every material point. We accomplish this by means of a nonlinear finite element analysis (FEA) using ABAQUS. The FEA analysis uses a special user-defined material subroutine by HKS/WEST customized for Nitinol. The loading condition on the stents can come from two sources: 1. An analytical approach to determine the stent diameters by balancing the stent within a 6% compliant tube to simulate physiological loading, or 2. A direct measurement of stent diameter change inside the tube from the in-vitro testing. This article demonstrates the criterion using the second approach, i.e., the measured stent diameters are used as the FEA input. The mean and alternating strains at every element integration point or when extrapolated at every node produces a single point in the mean and alternating strain plane. The discretized stent produces “point clouds”. When this “point cloud” plot is superimposed on the fatigue endurance limit, the designer will have an idea of the relative safety of the design. The results are compared with the linear approach using traditional beam theory. It is verified that when the deformation is small, the beam theory agrees well with the nonlinear FEA analysis.