FEM analyze for an arterial implant device.

Gheorghiu, Horia ; Chircor, Lidia ; Nicodim, Mariana 等

1. INTRODUCTION

Stents are small scaffold-like structures, placed inside occluded blood vessels to restore the vascular lumen and flow conditions. The mechanical performance of stents is dependent on the geometrical design, material employed and fabrication technology used. Typical stent designs can be categorized as follows: metallic mesh balloon-expandable stents (expanded by inflation of an angioplasty balloon), elastic and shape memory self-expandable stents (expanded by temperature change), silicone, and biodegradable devices (ANSYS, 2007). Common fabrication methods used to manufacture stents include laser cutting, braiding, and stereo lithography (Suresh, 1998).

This paper presents numerical results predicted by a simulation methodology for the crimping, deployment and in-vivo performance of a particular type of stent design. Typically a stent is mounted and crimped onto a balloon catheter, which is followed by a PTCA (Percutaneous Transluminal Coronary Angioplasty) procedure.

The stent is then positioned in the dilated artery by passing it through vasculature mounted onto a PTCA balloon catheter. When the balloon is correctly positioned the stent is deployed by inflating the balloon.

With the stent fully deployed the balloon catheter is deflated and removed from the vasculature.

The stent considered in this paper is assumed to be manufactured by laser-cutting the mesh pattern into an annealed 316L stainless steel tube (Bunea & Nocivin, 1999).

The resulting mesh is then electro-polished to give a smooth surface finish (ANSYS, 2007). The stent will remain implanted in the artery for the lifetime of the patient, during which the stent will undergo cyclic loading as a result of the variation of blood pressure due to the beating of the patient's heart.

For the purposes of the fatigue evaluation the pressure variation in the coronary arteries resulting from the beating heart is assumed to be 100-mmHg. It is also assumed that the entire pressure load is transferred from the artery to the stent. Both of these assumptions are very conservative for diseased coronary arteries.

The finite element method is used to analyze the crimping, deployment and fatigue loading in the stent geometry by two-dimensional (2D) finite elements.

[FIGURE 1 OMITTED]

2. DEVELOPMENT OF 2D FINITE ELEMENTS MODEL

2.1. Material Properties

The level of stress and strain defines the severity of loading of the material in a component. Metals normally have a region in which the strain is directly proportional to stress. In this region the material is said to be linear elastic. The limit of the linear elastic region is called the proportional limit. The strains accumulated at stresses higher than the proportional limit are not elastic (these are referred to as inelastic or plastic strains) because they remains when the material is unloaded. This is the material mechanism by which the stent is able to keep an artery open. Plastic strains accumulate as the stent is expanded by a balloon and remain when the balloon is removed, thereby keeping the stent deployed.

It is assumed that the stent under consideration in this paper is manufactured from 316L stainless steel. Young's modulus was taken as 207 GPa and Poisson's ratio was assumed to be 0.3 (Dieter, 1987).

2.2 Identification of Stent Geometry and Analysis Stages

The selected stent geometry analyzed in this paper is shown in Figure 1a. This design was developed by researchers at GMIT and as with commercially available stents (Suresh, 1998) it processes both axial and circumferential periodic symmetry. The presence of this symmetry implies that the analyses may be restricted to the repeating cell unit as shown in Figure 1b.

The stages of the stent's load history may be broken down into the following load steps:

Load Step 1. Crimping of the stent to a crimped diameter of 1.6 mm.

Load Step 2. Remove crimping tool and allow stent to spring-back to its equilibrium diameter.

Load Step 3. Expansion of the stent to its deployment diameter by inflation of internal balloon to a diameter of 4.25 mm.

[FIGURE 2 OMITTED]

Load Step 4. Remove balloon and allow spring-back of the stent to its new equilibrium diameter.

Load Step 5. Apply pulsatile loading on the outer surface of the stent with a cyclic pressure equivalent to 100 mmHg.

The residual stresses remaining after the first four steps as well as the pulsatile loading in Load Step 5 were used to calculate mean and alternating stresses for the cyclic loading of the stent. These were subsequently plotted on a Goodman diagram to predict the fatigue factor of safety of the stent.

3. FATIGUE LIFE CALCULATIONS

A stent is required to function under high cycle fatigue conditions. Regulatory authorities insist on numerical and experimental evidence that the proposed stent is capable of withstanding at least 400 million cycles of stress. In the results presented in this paper, a 'stress-life' approach was taken for the fatigue life prediction (Fung, 1993). This approach is further supported by the fact that the analysis predicts that no plastic straining takes place during the cyclic loading. Factors of safety were calculated for each model by employing the following formula:

n = [S.sub.a]/[[sigma].sub.a] (1)

where: n = fatigue factor of safety,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[[sigma].sub.min] is the residual stresses after the deployment is completed, [[sigma].sub.max] is the sum of the residual stresses after the deployment and the oscillating stresses resulting from the pressure loading, [S.sub.e] is the fatigue endurance limit of 316L, [S.sub.UT] is the Ultimate Tensile strength of 316L.

4. CONCLUSIONS & RESULTS

The 2D model presented in this paper is a two dimensional representation of a three dimensional structure. Therefore out of plane effects such as fish-scaling are assumed to be insignificant for the two dimensional model. In developing the 2D model the following procedure was used: Consider the stent structure as having a radius r, the repeating unit subtends an angle[phi], equal to 360/nrep, where nrep represents the number of the repeating units in the circumferential direction. This implies that the arc length of the curved repeating unit is [r.sub.[phi]]. Now consider that the repeating unit is deployed by an amount [[delta].sub.r], the angle [phi] must remain the same which implies that the arc length of the repeating unit will increase to (r+[delta]r)[phi]. These could be represented in a 2D space as two straight sections having these calculated development lengths.

A mesh convergence study was completed for the 2D models, which helped to identify the optimum mesh density distribution for this type of analysis, which yielded accurate results in acceptable CPU times.

A study was conducted in order to find the optimum mesh density to be used in the 2D analysis. A total of seven mesh densities were investigated. Figure 4 present the variation in the maximum of von Mises stress in the U strut as the total number of degrees of freedom (which is related to the mesh density) increases.

The variation of the stress levels from when the stent is crimped to when the pulsatile loads are applied is presented below. Stress-history plots are presented which indicate the von Mises stress, 1st Principal stress (tension) and 3rd Principal stress (compression)

5. REFERENCES

ANSYS Help System Online Documentation, 2007, ANSYS Inc., 275 Technology Drive, Canonsburg, PA 15317, USA

Bunea, D., Nocivin, A., (1999). Implant Materials, Printech Ed., Bucharest, ISBN 973-9475-85-X

Dieter, G.E., (1987). Mechanical Metallurgy, SI Metric Ed., McGraw-Hill Book Co., Singapore,, ISBN 0-07-100406-8

Fung, Y.C., (1993). Biomechanics--Mechanical Properties of Living Tissues, Second Ed., Springer, ISBN 0-387-97947-6 (New York).--ISBN 3-540-97947-6 (Berlin).

Suresh, S., (1998). Fatigue of Materials, 2nd Ed. Cambridge University Press, ISBN 0521578477