Biaxial Mechanical Properties of the Native and Glutaraldehyde-Treated Aortic Valve Cusp: Part II—A Structural Constitutive Model

[+] Author and Article Information
Kristen L. Billiar

Department of Biomedical Engineering, University of Miami, Coral Gables, FL 33124

Michael S. Sacks

Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15261

J Biomech Eng 122(4), 327-335 (Mar 22, 2000) (9 pages) doi:10.1115/1.1287158 History: Received May 25, 1999; Revised March 22, 2000
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.


Krucinski,  S., Vesely,  I., Dokainish,  M. A., and Campbell,  G., 1993, “Numerical Simulation of Leaflet Flexure in Bioprosthetic Valves Mounted on Rigid and Expansile Stents,” J. Biomech., 26, pp. 929–943.
Christie, C. W., and Medland, I. C., 1982, “A Non-linear Finite Element Stress Analysis of Bioprosthetic Heart Valve,” Finite Element in Biomechanics, Gallagher, R. H., Simon, B. R., Johnson, P. C., and Gross, J. F., eds., Chichester, Wiley, pp. 153–179.
Lee,  J. M., Courtman,  D. W., and Boughner,  D. R., 1984, “The Glutaraldehyde-Stabilized Porcine Aortic Valve Xenograft. I. Tensile Viscoelastic Properties of the Fresh Leaflet Material,” J. Biomed. Mater. Res., 18, pp. 61–77.
Lee,  J. M., Boughner,  D. R., and Courtman,  D. W., 1984, “The Glutaraldehyde-Stabilized Porcine Aortic Valve Xenograft. II. Effect of Fixation With or Without Pressure on the Tensile Viscoelastic Properties of the Leaflet Material,” J. Biomed. Mater. Res., 18, pp. 79–98.
Vesely,  I., and Noseworthy,  R., 1992, “Micromechanics of the Fibrosa and the Ventricularis in Aortic Valve Leaflets,” J. Biomech., 25, pp. 101–113.
Broom, N., and Christie, G. W., 1982, “The Structure/Function Relationship of Fresh and Gluteraldehyde-Fixed Aortic Valve Leaflets,” Cardiac Bioprosthesis, Cohn, L. H., and Gallucci, V., eds., Yorke Medical Books, New York, pp. 477–491.
Christie,  G. W., 1992, “Anatomy of Aortic Heart Valve Leaflets: The Influence of Glutaraldehyde Fixation on Function,” Eur. J. Cardio-Thoracic Surg., 6, pp. S25–S33.
Hilbert,  S., Barrick,  M., and Ferrans,  V., 1990, “Porcine Aortic Valve Bioprosthesis: A Morphologic Comparison of the Effects of Fixation Pressure,” J. Biomed. Mater. Res., 24, pp. 773–787.
Mayne,  A. S. D., Christie,  G. W., Smaill,  B. H., Hunter,  P. J., and Barratt-Boyes,  B. G., 1989, “An Assessment of the Mechanical Properties of Leaflets From Four Second-Generation Porcine Bioprosthesis With Biaxial Testing Techniques,” J. Thorac. Cardiovasc. Surg., 98, pp. 170–180.
Christie,  G. W., and Barratt-Boyes,  B. G., 1995, “Age-Dependent Changes in the Radial Stretch of Human Aortic Valve Leaflets Determined by Biaxial Stretching,” Ann. Thoracic Surg., 60, pp. S156–S159.
Brossollet,  L. J., and Vito,  R. P., 1996, “A New Approach to Mechanical Testing and Modeling of Biological Tissues, With Application to Blood Vessels,” ASME J. Biomech. Eng., 118, pp. 433–439.
Billiar,  K., and Sacks,  M., 2000, “Biaxial Mechanical Properties of Fresh and Glutaraldehyde Treated Porcine Aortic Valve Cusps: Part I—Experimental Findings,” ASME J. Biomech. Eng., 122, pp. 23–30.
Rousseau,  E. P. M., Sauren,  A. A. H. J., Van Hout,  M. C., and Van Steenhoven,  A. A., 1983, “Elastic and Viscoelastic Material Behaviour of Fresh and Glutaraldehyde-Treated Porcine Aortic Valve Tissues,” J. Biomech., 16, pp. 339–348.
Sauren,  A., van Hout,  M., van Steenhoven,  A., Veldpaus,  F., and Janssen,  J., 1983, “The Mechanical Properties of Porcine Aortic Valve Tissues,” J. Biomech., 16, pp. 327–337.
Sacks,  M. S., Smith,  D. B., and Hiester,  E. D., 1998, “The Aortic Valve Microstructure: Effects of Trans-Valvular Pressure,” J. Biomed. Mater. Res., 41, pp. 131–141.
Fung, Y. C., 1993, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York.
Humphrey,  J. D., Strumpf,  R. K., and Yin,  F. C. P., 1990, “Determination of a Constitutive Relation for Passive Myocardium: I. A New Functional Form,” ASME J. Biomech. Eng., 112, pp. 333–339.
Humphrey,  J. D., Strumpf,  R. K., and Yin,  F. C. P., 1992, “A Constitutive Theory for Biomembranes: Application to Epicardial Mechanics,” ASME J. Biomech. Eng., 114, pp. 461–466.
May-Newman,  K., and Yin,  F. C. P., 1998, “A Constitutive Law for Mitral Valve Tissue,” ASME J. Biomech. Eng., 120, pp. 38–47.
Sacks, M. S., 2000, “A Structural Constitutive Model for Chemically Treated Planar Connective Tissues Under Biaxial Loading,” Comput. Mech., in press.
Sacks, M., 1999, “A Structural Model for Chemically Treated Soft Tissues,” 1999 Advances in Bioengineering, ASME BED-Vol. 43, pp. 101–102.
Lanir,  Y., 1983, “Constitutive Equations for Fibrous Connective Tissues,” J. Biomech., 16, pp. 1–12.
Lanir,  Y., 1979, “A Structural Theory for the Homogeneous Biaxial Stress–Strain Relationships in Flat Collageneous Tissues,” J. Biomech., 12, pp. 423–436.
Harkness,  M., and Harkness,  R., 1959, “Effect of Enzymes on Mechanical Properties of Tissues,” Nature (London), 183, pp. 1821–1822.
Humphrey,  J. D., and Yin,  F. C. P., 1987, “A New Constitutive Formulation for Characterizing the Mechanical Behavior of Soft Tissues,” Biophys. J., 52, pp. 563–570.
Vesely,  I., Boughner,  D. R., and Leeson-Dietrich,  J., 1995, “Bioprosthetic Valve Tissue Viscoelasticity: Implications on Accelerated Pulse Duplicator Testing,” Ann. Thoracic Surg., 60, pp. S379–S383.
Nielsen,  P. M. F., Hunter,  P. J., and Smaill,  B. H., 1991, “Biaxial Testing of Membrane Biomaterials: Testing Equipment and Procedures,” ASME J. Biomech. Eng., 113, pp. 295–300.
Thubrikar, M., 1990, The Aortic Valve, CRC, Boca Raton.
Billiar,  K. L., and Sacks,  M. S., 1997, “A Method to Quantify the Fiber Kinematics of Planar Tissues Under Biaxial Stretch,” J. Biomech., 30, 753–756.
Sacks,  M. S., 1999, “A Method for Planar Biaxial Testing That Includes In-Plane Shear,” ASME J. Biomech. Eng., 121, pp. 551–555.
Lanir,  Y., Lichtenstein,  O., and Imanuel,  O., 1996, “Optimal Design of Biaxial Tests for Structural Material Characterization of Flat Tissues,” ASME J. Biomech. Eng., 118, pp. 41–47.
Zioupos,  P., and Barbenel,  J. C., 1994, “Mechanics of Native Bovine Pericardium: II. A Structure Based Model for the Anisotropic Mechanical Behavior of the Tissue,” Biomaterials, 15, pp. 374–382.
Spencer, A. J. M., 1980, Continuum Mechanics, Longman Scientific & Technical, New York.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1988, Numerical Recipes in C, Cambridge University Press, Cambridge.
Choi,  H. S., and Vito,  R. P., 1990, “Two Dimensional Stress–Strain Relationship for Canine Pericardium,” ASME J. Biomech. Eng., 112, pp. 153–159.
Humphrey,  J. D., Strumpf,  R. K., and Yin,  F. C. P., 1990, “Determination of a Constitutive Relation for Passive Myocardium: II—Parameter Estimation,” ASME J. Biomech. Eng., 112, pp. 340–346.
Billiar, K., 1998, “A Structurally Guided Constitutive Model for Aortic Valve Bioprostheses: Effects of Glutaraldehyde Treatment and Mechanical Fatigue,” Ph.D. Dissertation in Bioengineering, University of Pennsylvania, Philadelphia.
Fung,  Y. C., Fronek,  K., and Patitucci,  P., 1979, “Pseudoelasticity of Arteries of the Choice of Its Mathematical Expression,” Am. J. Physiol., 237, pp. H620–H631.
Yin,  F. C. P., Chew,  P. H., and Zeger,  S. L., 1986, “An Approach to Quantification of Biaxial Tissue Stress–Strain Data,” J. Biomech., 19, pp. 27–37.
Fung, Y. C., 1990, Biomechanics: Motion, Flow, Stress, and Growth, Springer-Verlag, New York.
Sacks,  M. S., and Chuong,  C. J., 1993, “A Constitutive Relation for Passive Right-Ventricular Free Wall Myocardium,” J. Biomech., 26, pp. 1341–1345.
Sacks, M. S., Smith, D. B., Thornton, M., and Iyengar, A. K. S., 1999, “Real Time Deformation of the Bioprosthetic Heart Valve,” Proc. First Joint BMES/EMBS Conference, Atlanta, GA, IEEE, p. 173.
Sacks, M. S., 1999, “A Structural Constitutive Model for Pericardium That Utilizes SALS-Derived Fiber Orientation Information,” ASME J. Biomech. Eng., submitted.
Hurschler,  C., Loitz-Ramage,  B., and Vanderby,  R., 1997, “A Structurally Based Stress–Stretch Relationship For Tendon and Ligament,” ASME J. Biomech. Eng., 119, pp. 392–399.
Comninou,  M., and Yannas,  I. V., 1976, “Dependence of Stress–Strain Nonlinearity of Connective Tissues on the Geometry of Collagen Fibers,” J. Biomech., 9, pp. 427–433.
Decraemer,  W. F., Maes,  M. A., and Vanhuyse,  V. J., 1980, “An Elastic Stress–Strain Relation for Soft Biological Tissues Based on a Structural Model,” J. Biomech., 13, pp. 463–468.
Shoemaker,  P. A., Schneider,  D., Lee,  M. C., and Fung,  Y. C., 1986, “A Constitutive Model for Two-Dimensional Soft Tissues and Its Application to Experimental Data,” J. Biomech., 19, pp. 695–702.
Sacks,  M. S., and Chuong,  C. J., 1992, “Characterization of Collagen Fiber Architecture in the Canine Central Tendon,” ASME J. Biomech. Eng., 114, pp. 183–190.
Oomens,  C. W. J., Ratingen,  M. R. V., Janssen,  J. D., Kok,  J. J., and Hendriks,  M. A. N., 1993, “A Numerical–Experimental Method for a Mechanical Characterization of Biological Materials,” J. Biomech., 26, pp. 617–621.
Trowbridge,  E. A., and Crofts,  C. E., 1986, “The Standardization Gauge Length: Its Influence on the Relative Extensibility of Natural and Chemically Modified Pericardium,” J. Biomech., 19, pp. 1023–1033.
Hoffman,  A. H., and Grigg,  P., 1984, “A Method for Measuring Strains in Soft Tissue,” J. Biomech., 10, pp. 795–800.
Humphrey,  J., Vawter,  D., and Vito,  R., 1987, “Quantification of Strains in Biaxially Tested Soft Tissues,” J. Biomech., 20, pp. 59–65.


Grahic Jump Location
Representative response of the components of deformation gradient tensor Fij1, κ1, κ2, and λ2, where subscripts 1 and 2 correspond to the circumferential and radial axes, respectively) during the loading phase of a biaxial test. Note the significant in-plane shear values (κ1 and κ2), which are plotted using a different scale.
Grahic Jump Location
Mean stress–strain response of the AV cusps under equibiaxial tension for the native and 0 and 4 mmHg glutaraldehyde-treated tissue. Note the difference in the biaxial response between the 0 and 4 mmHg demonstrating how the state of collagen fiber crimp during fixation can influence the mechanical response.
Grahic Jump Location
Stress–strain curves for six of the seven loading protocols for a 4 mmHg fixed specimen (open circles) and the simulated stress–strain curves (lines) using the optimal parameters (Table 1). The structural constitutive model demonstrated an excellent fit to the data, including the presence of large negative circumferential strains due to strong axial coupling. Although protocol five was not shown for clarity of presentation, it also demonstrated an equally good agreement between theory and experiment. Inset: biaxial testing protocols with the corresponding protocol numbers shown for reference.
Grahic Jump Location
Simulation of the effect of misalignment of the biaxial test specimen to testing axes by setting μ=10 deg, demonstrating a large change in peak extensibilities, especially in the radial direction. This result underscores the need for complete deformation state analysis and compensation of small misalignments when studying highly aligned fibrous tissues such as the AV cusp.
Grahic Jump Location
Effective fiber stress–strain curves calculated using Eq. (2) from 0 to 60 N/m and the A* and B values in Table 1. Native and 0 mmHg fixed tissue had relatively similar responses, whereas the loss of collagen fiber crimp by the application pressure during glutaraldehyde treatment clearly decreased the effective fiber compliance in the 4 mmHg fixed group. Also shown is the result for the 4 mmHg specimens re-analyzed with μ=0. Although smaller than the pressure fixation effects, this left shift in the stress–strain curve demonstrates how inaccuracies in the parameter values can be introduced when small misalignments are not accounted for when studying highly aligned fibrous tissues.
Grahic Jump Location
Simulations using the structural model of the effect of σ on the equibiaxial stress–strain behavior. The insets provide a graphic representation of the fiber probability density distribution for each σ value: (a) σ=90 deg, approximately isotropic, (b) σ=35 deg, response qualitatively similar to bovine pericardium, (c) σ=20 deg, the circumferential strains are negative at low equibiaxial tensions, and (d) σ=10 deg, the material behavior is highly anisotropic. The dotted lines indicating zero strain are included to highlight ability of the model to simulate the crossover to negative strain observed in the pressure fixed cusps subjected to equibiaxial tension.
Grahic Jump Location
A representative R(θ) distribution from an AV cusp fit to a dual Gaussian distribution using the methods of Sacks and Chuong 48. Here, the AV cusp fiber orientation distribution was principally composed of a highly aligned population (σ1=16 deg) and a broader distribution (σ2=44 deg). Although the fibers of both populations contribute to R(θ), the mechanical contribution of the fibers belonging to σ2 was negligible, supporting our assumption that the in-plane biaxial response can be modeled by a single highly aligned fiber population within the cusp.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In