Reliable Numerical Models of Nickel-Titanium Stents: How to Deduce the Specific Material Properties from Testing Real Devices

Abstract

The current interest of those dealing with medical research is the preparation of digital twins. In this frame, the first step to accomplish is the preparation of reliable numerical models. This is a challenging task since it is not common to know the exact device geometry and material properties unless in studies performed in collaboration with the manufacturer. The particular case of modeling Ni-Ti stents can be highlighted as a worst-case scenario due to both the complex geometrical features and non-linear material response. Indeed, if the limitations in the description of the geometry can be overcome, many difficulties still exist in the assessment of the material, which can vary according to the manufacturing process and requires many parameters for its description. The purpose of this work is to propose a coupled experimental and computational workflow to identify the set of material properties in the case of commercially-resembling Ni-Ti stents. This has been achieved from non-destructive tensile tests on the devices compared with results from Finite Element Analysis (FEA). A surrogate modeling approach is proposed for the identification of the material parameters, based on a minimization problem on the database of responses of Ni-Ti materials obtained with FEA with a series of different parameters. The reliability of the final result was validated through the comparison with the output of additional experiments.

Keywords: Digital twin; Material identification; Model validation; Self-expandable stent; Surrogate modeling.

Figure 1

(a) Ni–Ti stress/strain curve in tension and compression according to the Abaqus super-elastic material module. See Nomenclature for the meaning of each parameter; (b) reference behavior for the virtual case: the global force was plotted against the number of time increments. Phase I is defined as the first 10 increments, Phase II is comprised between the 11th and the 50th increment while Phase III lasts from the 51st to the end (100th).

Figure 2

(a) The stent COMP geometry with detail of (b) the functional unit; (c) the stent ABS and (d) its functional unit. For both stents, insight into the constrained surfaces of the functional units is given.

Figure 3

(a) Tensile force-displacement curves of stent COMP (black) and ABS (red), with a comparison between the numerical output obtained by simulating the whole stent (solid line) or the functional unit (dashed line) properly scaled; (b) tensile force-displacement curves obtained through the simulation of the COMP functional unit associated with Mat-1 and Mat-2.

Figure 4

Assessment of the validity of the GP models for the identification of the three phases through the leave-one-out method and SCVR: (a) Mat-1 and (b) Mat-2.

Figure 5

Representation of a slice of the response surface for Mat-1, showed according to the most relevant parameters, in the case of (a) Phase II (H fixed at 0.5) and (b) Phase III (E_M and ε_L fixed at 0.5).

Figure 6

Comparison between the tensile force-displacement curves obtained using the target and identified parameters in case of (a) Mat-1 and (b) Mat-2.

Figure 7

Comparison between the experimental (solid lines) tensile force-displacement curves and the numerical outputs (dashed lines) obtained using the identified set of parameters in case of stent COMP (black) and ABS (red).

Figure 8

Comparison between the experimental (solid lines) curves from the crush test and the numerical outputs (dashed lines) obtained using the identified set of parameters in case of stent COMP (black) and ABS (red).