DESIGN
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In the 1950s, two types of heart valves emerged: mechanical valves and tissue valves, each possessing distinct properties. Mechanical valves consist of a polymer or metallic system that allows for the forward flow of blood during systole and stops regurgitation during diastole. Mechanical valves provide long-term durability, but require lifelong anticoagulation treatment and present a significant departure from native valve hemodynamics. Additionally, the required medication treatments can be painful, and it is difficult for the patient to continue with a lifestyle similar to that before the implant.
Bioprosthetic tissue valves use tissue as a means to create leaflets that function in a manner very similar to native heart valves. Tissue valves tend to have limited durability in comparison with mechanical valves, but they provide superior hemodynamic behavior, minimal thrombosis, and better host response.
The design of heart valves involves optimizing leaflet size and geometry to obtain ideal functional performance of blood flow hemodynamics. Finite-element analysis (FEA) has been an important tool for valve design. It provides a fundamental understanding of key characteristics such as leaflet geometry, tissue thickness, and leaflet mismatch. It also provides a common understanding of what may happen as a result of nonconcentric valve deployment. Some areas of interest in the development of a tissue valve are in-plane leaflet stresses, deformation under loading, and magnitude of suture forces. By using FEA simulation in the tissue valve development process, key failure modes can be identified, and the durability of designs can be quantified. This article describes a representative case study example for leaflet geometry design, using FEA.
The following problems represent the perfect trifecta of solid mechanics: nonlinear material, large displacements or strains, and nonlinear boundary conditions. The use of software such as HyperWorks is a novel approach for optimizing a tissue valve design based on diastolic loading. The use of such tools has been well documented in the design of automotive, aerospace, and consumer products. However, its use in the world of developing implantable biomedical devices is relatively new.
Procedures
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Table I. (click to enlarge) Mechanical property test data for stress-strain of pericardial tissue. See Figure 2 for the stress-strain curve. |
The heart valve tissue was characterized using HyperWorks software, a suite of engineering software products that support product design feasibility and development studies. HyperMesh, a component within the HyperWorks suite, was used to create finite-element models to be used in conjunction with Abaqus standard version 6.5-3 as a solver. Abaqus is a suite of general-purpose nonlinear FEA programs. Run times were approximately 1.4 hours on a 64-bit Linux 2-node cluster.
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Figure 1. (click to enlarge) Valve geometry model in ProE 2.0 (a) and leaflet mesh in HyperWorks 7.0 (b). |
Finite sliding with penalty stiffness was modeled. Overclosure was also implemented to stabilize the contact between the leaflets by providing a buffer region to initialize the creation of forces across contact pairs. The process enabled gradual reduction of size per increment, rather than having significant size change per iteration. Such care can be attributed to surface elements now being accounted for on both sides of the contact pair. Hourglass control was instantiated as part of the S4R shell formulation, where elements were described in Abaqus as “4-node doubly curved general-purpose shell, reduced integration with hourglass control, finite membrane strains.” S4R is a type of shell element that uses reduced integration. Hourglass control is required for these elements because of the possibility of having hourglass deformation taking place, which is due to their inherent formulation.
Across the thickness of the specimen, one integration point was used with reduced integration shell elements. The integration point was located at the mid-thickness distance. At that time, it was not feasible to use fully integrated shell elements with the hyperelastic material model. Some amount of stabilization was instilled model-wide and for the contacts. This stabilization on the global model adds nodal viscous forces if instabilities exist at some point during the solution within Abaqus. Stabilization within the contact is used to dampen the chattering and stick or slip nature of a contact pair.
A limiting factor for the amount of stabilization force on nodes was set. The stabilization factor was selected; the stabilization energy equated to ~3.0% of the total internal strain energy. It evolved early in the simulation and remained level for the remainder of the step. To ensure balance of the stabilization feature, another model was run with an order of magnitude of a factor of 2 larger. The results provided a difference of less than 2% in the maximum stress value.
Geometry
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Figure 2. (click to enlarge) Stress-strain curve for pericardial tissue. See Table I for mechanical property test data. |
Valve geometry was created by first taking a laser scan image of a silicone valve cast. The raw point cloud data were collected from the laser scanner and postprocessed to minimize noise and to give an acceptable overview of the endocardial outflow surface of the valve. Pro-E software was employed to build a parameterized CAD model of the valve being investigated using the scanned data. The final CAD model characterized the leaflets of the valve along with the surrounding conduit in which the valves were attached. The Pro-E file was then imported into HyperMesh where the remaining FEA model setup occurred (see Figure 1).
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Figure 3. The boundary condition setup for the FEA (a), the valve configuration (b), and the top view showing the leaflet stresses (c). Arrows indicate a direction of constrained translational degree of freedom. |
Approximately 20,500 large strain-reduced integration shell elements (S4R) were used to model both the conduit and valve leaflets. This type of element was used in order to capture both in-plane strains as well as to account for bending stiffness in important regions, such as the central coaptation region. This shell element formulation has been used by a number of other investigators.1 Approximately 775 SPRINGA elements were used to fasten the leaflets to the surrounding conduit based on the design iteration being investigated. These elements were used to simulate the sutures that fasten the leaflets to the conduit. They provide a tension-only load transfer, which most closely represents how sutures act in authentic valves.
FEA Model Setup
A hyperelastic isotropic material model was used for both the valve leaflets and the conduit. This model was chosen because it best fits the uniaxial tensile tissue testing data, and it has successfully modeled prosthetic heart valves (see Figure 2).2
The material properties were obtained from generic fixed pericardial tissue by uniaxial tensile testing. This testing found similar test data to that in literature.3 Although it is understood that tissue may be anisotropic, for this initial investigation only isotropic properties were defined. Future work may include the use of structural models and biaxial test data as investigated by Driessen et al.4
The hyperelastic material model assumes isotropic and nonlinear properties. This model is commonly used for materials that display elastic responses up to large strains (see Equations 1 through 3).5
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Figure 4. (click to enlarge) Shown above: a valve with flat, free-margin leaflet configuration tensile stress (a) and a valve with compressive stress (b). |
The large strain deformations can cause distortions of the geometry. The isotropic hyperelastic model can be written as a function of the Cauchy-Green tensor. Malvern showed that the recoverable strain energy density per unit volume (see Equation 1) is a function of the deviatoric strain invariants (see Equation 2), where U is the strain energy per unit of reference volume and Jel is the elastic volume defined by the ratio of total volume and thermal expansion volume.6
The hyperelastic material model can be written as defined by Mooney and Rivlin, where Cij and k are determined from experimental data:7,8
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As predicted, commissure sutures pull out from valve geometry with flat, free margins used for model validation. |
Contact definition was set up between all leaflets so that they would bear load together under diastolic loading conditions. Boundary conditions consisted of fixing all degrees of freedom around the circumference of the proximal and distal ends of the conduit. Distributed pressure loads were applied to all inflow and outflow surfaces during peak diastole, as shown in Figure 3. The magnitude of the pressures applied on both inflow and outflow surfaces were determined from ovine models with implanted bioprosthetic valves. The results of interest were the global deformation mode, the loads on sutures, and the stresses and strains on the surrounding conduit of the valve.
Results and Discussion
Tissue Valve Analysis. It is universally known from literature that flat, free margins provide the highest loading stresses in the aortic valve.9 Therefore, a valve with leaflets containing a flat, free-margin shape was studied as a control group in order to validate the model. The FEA estimated the leaflet tensile and compressive stresses as 0.60 and –0.819 MPa, respectively, (see Figure 4). Different leaflet lengths and shapes can be evaluated to minimize the leaflet stresses, which essentially improves valve durability.
Numerical simulation validations are difficult because experimental measurements cannot obtain accurate readings close to the leaflets and valve housing.10 Verification of the model was performed by building valves with the same leaflet configuration and conducting accelerated wear testing on them in a simulated physiological environment. The valves were tested to an estimated 200 million cycles and observed at 20-million-cycle increments. The valves built with the flat, free-margin leaflet geometry showed wear on the commissures, which correlated to the FEA model predictions of high stresses at the commissures.
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Figure 5. (click to enlarge) Estimated conduit stresses for valve with flat, free-margin leaflets. |
Conduit Analysis. Stresses vary across the valve and the root, which is likely caused by their inherent morphological asymmetry and stress sharing.11 Therefore, another analysis was conducted to look specifically at the stresses in the conduit. Surface-to-surface contact was used when analyzing leaflet to conduit contact. To reduce trauma to the conduit, a minimal conduit stress is desired. As seen in Figure 5, the commissure regions are the locations for the highest stress, 1.90 MPa, and would likely cause suture pullout at the commissures.
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Figure 6. (click to enlarge) Estimated suture loads for valve with flat, free-margin leaflets, where locations 1–3 represent different sutures along the valve. |
Suture-Force Analysis. The valve leaflets were sewn to a tissue conduit via polyester threaded sutures. The suture loads can be determined as shown in Figure 6. The maximum suture load for the case study was calculated to be 0.0432 N. Tissue attachment methods could also affect the suture loads and transference of stresses to the valve. Lim and Cheong found that suturing weakens the tissue by being more extensible and lowering the stress at rupture.12 Therefore, future investigations of influential parameters such as stitch placement, suture type, suture diameter, stitch type, and stitch distance and depth should be considered for valve modeling.
Conclusion
An FEA model was used to simulate a tissue heart valve in order to obtain a thorough understanding of the mechanics, and the complex tissue properties that contribute to better valve performance. Valve characteristics such as tensile and compressive leaflet stresses, conduit stresses, and suture loads were calculated. For the first time, such software was used for biomedical heart valve applications, and it provided adequate meshing and solver resolution. Future work will involve a complete fluid structure interaction analysis to assess whether blood and fluid have a long-term effect on the structural behavior of valve leaflets. In conclusion, optimal leaflet shapes that minimize stresses on the leaflets can be identified for various valve applications using FEA.
Melissa Denton is principal R&D engineer for Medtronic (Santa Ana, CA), and Steven Ford is lead engineer of a product development group at Altair Engineering (Irvine, CA). Contact him at sford@altair.com
References
1. J Li, , XY Luo, and ZB Kuang, “A Nonlinear Anisotropic Model for Porcine Aortic Heart Valves,” Journal of Biomechanics 34, no. 10: 1279–1289.
2. MA Thorton, IC Howard, and EA Patterson, “Three-Dimensional Stress Analysis of Polypropylene Leaflets for Prosthetic Heart Valves,” Medical Engineering & Physics 19, no. 6: 588–597.
3. WA Naimark et al., “Correlation of Structure and Viscoelastic Properties in the Pericardia of Four Mammalian Species,” American Journal of Physiology: Heart and Circulatory Physiology (1992): 0363-6135: H1095- H1106.
4. NJ Driessen, et al., “Computational Analyses of Mechanically Induced Collagen Fiber Remodeling in the Aortic Heart Valve,” Journal of Biomechanical Engineering, V 125, no. 4: 549–557.
5. ABAQUS Analysis User’s Manual, version 6.7, (Suresnes, France: Dassault Systemes, 2007): 17.4.1.1–17.4.1.25.
6. LE Malvern, Introduction to the Mechanics of a Continuous Medium, (New York: Prentice-Hall, 1969).
7. M Mooney, “A Theory of Large Elastic Deformation,” Journal of Applied Physics V, no. 11: 582–592.
8. RS Rivlin and DW Saunders, “Large Elastic Deformations of Isotropic Materials, VII, Experiments on the Deformation of Rubber,” Transactions of the Royal Society of London, Series A (Mathematical and Physical Sciences) V, no. 243: 251–288.
9. M Thubrikar, The Aortic Valve, (Boca Raton, FL, CRC Press: 1990): 119–126.
10. W Sun, A Abad, and MS Sacks, “Simulated Bioprosthetic Heart Valve Deformation under Quasi-Static Loading,” Journal of Biomechanical Engineering 914, no. 127: 905.
11. K Grande et al., “Stress Variations in the Human Aortic Root and Valve: The Role of Anatomic Asymmetry,” Annals of Biomedical Engineering V, no. 26: 543–545.
12. KO Lim and KC Cheong, “Effect of Suturing on Mechanical Properties of Bovine Pericardium Implications for Cardiac Valve Bioprosthesis,” Medical Engineering and Physics V, no. 16: 526–530.
