Finite Element Analysis of a Percutaneous Stent-Mounted ... · PDF fileFinite Element Analysis...

2004 ABAQUS Users’ Conference 209

Finite Element Analysis of a Percutaneous Stent-Mounted Heart Valve

Milton A. DeHerrera, Ph.D., Ninh Dang, B.S.

Edwards Lifesciences LLC

One Edwards Way Irvine, CA 92614

Abstract: The current medical procedure for cardiac valve replacement requires an operation to open the chest (thoracotomy) and cardiopulmonary bypass (hookup to a heart-lung machine). Each year, an estimated 300,000 patients worldwide undergo these invasive open-heart procedures. These procedures are neither practical nor recommended for patients who are of an advanced age, have co-morbidity conditions and/or are not in good health. Recent developments have raised the possibility of percutaneous or endovascular implantation of a stent-mounted heart valve on a catheter-based delivery system, which would serve this unmet need for non-surgical candidates for open-heart surgery. The technical and clinical issues to be resolved are overwhelming, but once understood these promising new designs might someday be the procedure of choice for heart valve replacement providing an attractive alternative to the clinically proven but more invasive open-heart surgery procedure. One of the proposed valve designs was that of a flat-sheet based stent. This stent-mounted valve would be rolled up to about a 20 French (6.66mm OD) size and delivered percutaneously. Because of the physical and physiological constraints, NiTinol was chosen for the sheet material. An analysis of the sheet roll-down and radial pressure loading was performed using ABAQUS and NiTinol UMAT/VUMATs’ developed by ABAQUS West. Results of the analyses are shown and conclusions regarding the mechanical adequacy of this valve are presented. Keywords: ABAQUS Explicit, ABAQUS Standard, Cardiovascular Therapy, Contact, Double-Sided Contact, Heart Valve Replacement, Minimally Invasive Surgery, Mass Scaling, Nitinol, Percutateous Stent Delivery, Quasi-Static Analysis, Self-Contact, Superelastic Materials, UMAT, VUMAT.

1. Introduction In the United States and in many parts of the world, Cardiovascular Disease (CVD) is the leading cause of natural death. Nearly one million people died of CVDs in the United States alone in 2001, more than the next five leading causes of death combined (see Figures 1 and 2). CVDs have been the leading cause of death in the US every year since 1900, except for 1918, the year of the Great Influenza Pandemic. The annual costs of CVDs are estimated to be in the hundreds of billions of dollars (AHA, 2004). Cardiac surgery in its current form is highly invasive and generally requires a lengthy stay at the hospital by the patient. A principal objective in the Medical Device industry

210 2004 ABAQUS Users’ Conference

is to develop less invasive surgical procedures that minimize the physical trauma incurred when making “repairs” to the cardiovascular systems. It is believed that a collateral benefit of such procedures will be a significant reduction in a patient’s recovery time and ultimately, in healthcare costs.

2. Statement of the problem: Physiological point of view An important part of the Cardiovascular system is the Aortic Valve (AV) which, when it functions properly, efficiently helps transport the freshly oxygenated blood from the heart’s right ventricle into the circulatory system and prevents blood from flowing back into the ventricle. The AV can become impaired as result of calcification (calcium from the blood stream deposits or precipitates out onto the valve leaflets) and other chemical, physical, or biological mechanisms. In patients where an impaired AV leads to a severe cardiac deficiency, valve repair and/or valve replacement is generally called for. The current medical procedure for cardiac valve replacement requires an operation to open the chest (thoracotomy) and cardiopulmonary bypass (hookup to a heart-lung machine). Each year, an estimated 300,000 patients worldwide undergo these invasive open-heart procedures. Recovery time for a successful procedure is measured in weeks, and generally requires prolonged hospitalization. Furthermore, these procedures (thoracotomy and CP bypass) are neither practical nor recommended for patients who are of an advanced age, have co-morbidity conditions and/or are not in good health.

3. Statement of the problem: Materials Science point of view

During the late 1990’s, Edwards Lifesciences undertook an effort to produce a stent-mounted valve that could be delivered percutaneously, that is, through a blood vessel with an entry point being located in either the femoral artery, the carotid artery or the subclavian artery. Any system that is to be delivered percutaneously must meet the following minimum requirements:

o The entire system must fit in a geometric envelope of outer diameter 20 – 24 French (6.66mm – 8mm), preferably the former.

o The system must have enough radial stiffness to remain in place and maintains its circular shape after it is fully deployed.

o The peak tensile stress and strain during the device’s service life should be small enough so that material fatigue does not become a prosthesis valve performance issue.

It is difficult to find engineering materials that fit two of the above requirements, let alone all three. However, in the early 1990’s, materials known as Shape Memory Alloys (SMA’s) were introduced for various applications in the medical device industry, and these materials were considered promising for the aforementioned percutaneous system. The term “Shape Memory” reflects the fact that such materials “remember” the geometric configuration that they exist in at a higher temperature. In particular, the Nickel-Titanium alloy NiTinol showed great promise because of its uncanny ability to undergo large strains in its “soft” state and then revert back to its initial formed shape when the temperature of material was increased.


The initial concept for this prosthesis aortic valve was based on using a NiTinol flat-sheet with tissue leaflets sutured onto its inner surface. The NiTinol flat-sheet would be cooled down below its Martensitic Start temperature Ms. It is rolled down to a smaller diameter and geometrically confined to a 20 French size where it would stay until it was released into its deployed position, at which time the increased body temperature would cause a transformation into Austenite and thus revert the NiTinol flat-sheet back into its “original” circular shape. To ensure that the NiTinol flat-sheet could overcome the native calcification resistance, an inflatable and disposable balloon catheter within the lumen of the prosthesis is dilated to press and pin the native leaflets back against the aortic annulus. The diseased native leaflets are now held in check by the now cylindrical and slightly oversized prosthesis aortic valve, with the new valve leaflets working to restore normal aortic functions and cardiac outputs to the patient.

4. The NiTinol Superelastic material model

The ABAQUS NiTinol model is based on the work of Auricchio (1996,1997), Taylor and Lubliner (1996, 1997), with extensive extensions by Rebelo (2002). The model is defined by stress-strain curve and “breakpoint” stresses shown on Figure 3 and the thermomechanical variation curves shown on Figure 4. This model requires, among other things, two modulii of Elasticity, a plateau transformation strain, and five stress breakpoints. Below is a list of the input parameters required to run this model in ABAQUS: EA = Austenitic Elastic Modulus νA = Austenitic Poisson’s ratio EM = Martensitic Elastic Modulus νM = Martensitic Poisson’s ratio εL = Transformation strain (δσ/δT)L = Loading (δσ/δT) σS

L = Start of transformation stress during loading σE

L = End of transformation stress during loading T0 = Reference temperature (δσ/δT)U = Unloading (δσ/δT) σS

U = Start of transformation stress during unloading σE

U = End of transformation stress during unloading

5. Application of ABAQUS Standard and ABAQUS Explicit

The two principal questions that had to be answered by this study were: (1) What stresses and strains result when the NiTinol flat-sheet is rolled onto a pin? and (2) What is the radial strength/stiffness of the deployed prosthesis? When we first looked at this problem, the current release of Abaqus was version 6.2. To analyze the roll-down of the flat-sheet prosthesis required using advanced features like double-sided contact, self-contact and finite sliding contact. As a result, we decided that the best course of action was to use ABAQUS Explicit for the roll-down simulation of the flat-sheet and ABAQUS Standard to study the effect of a radially inward pressure on the final, deployed configuration.


The modeling process starts with a drawing of the flat-sheet pattern (Figure 5). A 2-D shell mesh is created on a de-featured version of this initial geometry (Figure 6). For the radial pressure analysis, the flat mesh is then mapped into a cylindrical mesh through a geometric transformation that depends on the length of the flat-sheet and the desired prosthesis diameter. The cylindrical mesh is shown on Figures 7 and 8. Figure 9 shows a picture of an unlocked prosthesis with attached leaflets Note that this is, geometrically, very close to the deployed configuration. Finally, for the roll-down analysis, the flat mesh shown on Figure 6 is constrained by three rigid bodies as will be shown in next section.

5.1 Simulation of flat-sheet prosthesis roll-down The roll-down of the flat-sheet was modeled by using one deformable body consisting of 5581 S3R and S4R elements and 6110 nodes, one rigid body to simulate the internal pin on which the flat-sheet is being rolled onto, and two guiding rigid bodies (Figures 10, 11). The analysis was run with ABAQUS Explicit, using variable mass scaling to dictate an initial time increment of 10-5

seconds (compared to an unscaled time increment of 4.9X10-8 sec). The problem was recently rerun on a 2-CPU 1.3GHz HP Itanium machine running HP-UX 11.2; total wall clock time was slightly over four hours. To verify that we were not overdoing the mass scaling, a plot of internal and kinetic energy was generated confirming that the KE was well below the IE (see Figure 12). Figure 13 shows a sequence of a contour plots of tensile strain LEP3 on the deformed geometry as the stent roll-down proceeds from right to left. Figure 14 shows the same contour plot sequence on the undeformed geometry. The resulting peak tensile strains in critical areas at the end of the roll-down were within acceptable bounds. ABAQUS Explicit was instrumental in the successful simulation of a fairly intricate contact problem.

5.2 Determination of flat-sheet prosthesis radial strength

Successful delivery and deployment of the prosthesis aortic valve would result in the lower part of the prosthesis being located in the aortic annulus. It was intended that the prosthesis would be oversized with respect to the diameter of the aortic annulus to ensure its fixation. We can study this aspect of the deployed configuration by applying a radially inward pressure on the lower part of the prosthesis, below the so-called “scallop line.” We studied various pressure load configurations and observed that this prosthesis did not have as much radial strength as other competing designs. There was significant prosthesis ovalization at pressures as low as 0.049 MPa (7.07psi) and outright collapse at about 0.055 MPa (8 psi). Figure 15 shows the original, undeformed configuration of a deployed prosthesis in its initial state, and Figure 16 shows the deformation incurred when the elements below the scallop line are given a radially inward pressure of 0.049 MPa (7.07 psi)


6. Discussion

It is well known from solid mechanics that the radial strength of shell structures depends on the R/t ratio, where R = shell radius and t = shell thickness (see Donnell, 1976). The prosthesis geometry analyzed had an R/t ≈ 60; we did not anticipate that the radial strength would be so low for this R/t. Without a change in the material specification, strengthening of the prosthesis could only be accomplished by increasing the shell thickness t, which would in turn have worked against the 20-24 French roll-down size limitation. As a result, this design was not considered to be a likely candidate for productization, and development was shelved before any significant testing efforts were spent by our company.

7. Conclusion

A two-pronged study of a flat-sheet based prosthesis was made using ABAQUS. Using the ABAQUS NiTinol superelastic material model we were able to show that the strains resulting from the roll-down of the prosthesis were within acceptable bounds. However, using the same numerical tools we found that the prosthesis was deficient in radial strength. Thus, through the use of ABAQUS we were able to show the inadequacy of this design without extensive and costly testing efforts in the benchtop and animal models.

8. References 1. “Heart Disease and Stroke Statistics, 2004 Update”, American Heart Association, 2004 2. Auricchio, F. and R.L. Taylor “Shape-Memory Alloys: Modeling and Numerical

Simulations of the Finite-Strain Superelastic Behavior.” Computational Methods in Applied Mechanics and Engineering 143 (1997), 175-194

3. Auricchio, F., R.L. Taylor and J. Lubliner “Shape-Memory Alloys: Macromodelling and

Numerical Simulations of the Superelastic Behavior.” Computational Methods in Applied Mechanics and Engineering 146 (1997), 281-312

4. Donnell, LH, Beams, Plates and Shells McGraw-Hill, 1976. 5. Lubliner, J. and F. Auricchio “Generalized Plasticity and Shape-Memory Alloys.”

International Journal of Solids and Structures 33 (1996), 991-1003 6. Rebelo, N. Private Communication, (2002)


Figure 1. US Mortality figures for the year 2001 (From AHA, 2004).

Figure 2. US Mortality figures based on gender for the year 2001 (From AHA, 2004)


Figure 3. Abaqus NiTinol Superelastic material model nomenclature.


Figure 4. Abaqus NiTinol Superelastic material model thermomechanical variation curves.


Figure 5. Drawing layout of a flat-sheet stent prototype.

Figure 6. Mesh of flat-sheet stent shown in Figure 5.


Figure 7. Undeformed mesh of deployed stent.

Figure 8. Undeformed mesh of deployed stent, element edges turned off.


Figure 9. Unlocked stent with attached leaflets.

Figure 10. Partial view of rigid bodies used to model flat-sheet stent roll-down.


Figure 11. Initial configuration of flat-sheet stent and rigid pin prior to roll-down.

Figure 12. Energy curves for flat-sheet stent roll-down analysis.


Figure 13. Maximum tensile strain LEP3 (mm/mm) during flat-sheet stent

roll-down.


Figure 14. Maximum tensile strain LEP3 (mm/mm) during flat-sheet stent

roll-down, displayed on undeformed configuration.


Figure 15. Undeformed configuration of deployed stent.

Figure 16. Deformed shape of deployed stent after application of a 0.049 MPa

(7.07 psi) radial pressure at all elements below the scallop line.

9. Acknowledgements Ms. Eileen Mahoney and Dr. Hengchu Cao helped with the proofreading and editing of this manuscript. Much insight on the functionality of this prosthesis was gained from the animal studies conducted by Dr. John Webb, MD of St. Paul’s Hospital in Vancouver, BC in Canada.

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