Computational Analyses of Mechanically Induced Collagen Fiber Remodeling in the Aortic Heart Valve

[+] Author and Article Information
Niels J. B. Driessen, Ralf A. Boerboom, Jacques M. Huyghe, Carlijn V. C. Bouten, Frank P. T. Baaijens

Eindhoven University of Technology, Department of Biomedical Engineering, Laboratory for Biomechanics and Tissue Engineering, PO Box 513, 5600 MB Eindhoven, The Netherlands

J Biomech Eng 125(4), 549-557 (Aug 01, 2003) (9 pages) doi:10.1115/1.1590361 History: Received July 25, 2002; Revised March 12, 2003; Online August 01, 2003
Copyright © 2003 by ASME
Topics: Fibers , Valves
Your Session has timed out. Please sign back in to continue.


Schoen,  F. J., and Levy,  R. J., 1999, “Tissue Heart Valves: Current Challenges and Future Research Perspectives,” J. Biomed. Mater. Res., 47(4), pp. 439–465.
Sodian,  R., Hoerstrup,  S. P., Sperling,  J. S., Daebritz,  S., Martin,  D. P., Moran,  A. M., Kim,  B. S., Schoen,  F. J., Vacanti,  J. P., and Mayer,  J. E., 2000, “Early in vivo Experience With Tissue-Engineered Trileaflet Heart Valves,” Circulation, 102(19), pp. III22–III29.
Hoerstrup,  S. P., Sodian,  R., Daebritz,  S., Wang,  J., Bacha,  E. A., Martin,  D. P., Moran,  A. M., Guleserian,  K. J., Sperling,  J. S., Kaushal,  S., Vacanti,  J. P., Schoen,  F. J., and Mayer,  J. E., 2000, “Functional Living Trileaflet Heart Valves Grown in vitro,” Circulation, 102(19), pp. III44–III49.
Sodian,  R., Hoerstrup,  S. P., Sperling,  J. S., Daebritz,  S., Martin,  D. P., Schoen,  F. J., Vacanti,  J. P., and Mayer,  J. E., 2000, “Tissue Engineering of Heart Valves: in vitro Experiences,” Ann. Thorac. Surg., 70(1), pp. 140–144.
Sauren, A. A. H. J., 1981, “The Mechanical Behavior of the Aortic Valve,” Ph.D. thesis, Technische Hogeschool Eindhoven.
Guidry,  C., and Grinnell,  F., 1985, “Studies on the Mechanism of Hydrated Collagen Gel Reorganization by Human Skin Fibroblasts,” J. Cell. Sci., 79, pp. 67–81.
Rubin, E., and Farber, J. L., 1998, Pathology, Lippincott-Raven, Philadelphia.
Christie, G. W., and Medland, I. C., 1982, “A Non-Linear Finite Element Stress Analysis of Bioprosthetic Heart Valves,” In: Gallagher, R. H., Simon, B. R., Johnson, P. C., and Gross, J. F., (eds.), Finite Elements in Biomechanics, Wiley, Chichester, pp. 153–179.
Li,  J., Luo,  X. Y., and Kuang,  Z. B., 2001, “A Nonlinear Anisotropic Model for Porcine Aortic Heart Valves,” J. Biomech., 34(10), pp. 1279–1289.
Peskin,  C. S., and McQueen,  D. M., 1994, “Mechanical Equilibrium Determines the Fractal Fiber Architecture of Aortic Heart Valve Leaflets,” Am. J. Physiol., 266(1), pp. H319–H328.
Cowin,  S. C., 1986, “Wolff’s Law of Trabecular Architecture at Remodeling Equilibrium,” J. Biomech. Eng., 108(1), pp. 83–88.
Cowin,  S. C., Sadegh,  A. M., and Luo,  G. M., 1992, “An Evolutionary Wolff’s Law for Trabecular Architecture,” J. Biomech. Eng., 114(1), pp. 129–136.
Dallon,  J. C., and Sherratt,  J. A., 1998, “A Mathematical Model for Fibroblast and Collagen Orientation,” Bull. Math. Biol., 60(1), pp. 101–129.
Dallon,  J. C., Sherratt,  J. A., and Maini,  P. K., 1999, “Mathematical Modelling of Extracellular Matrix Dynamics Using Discrete Cells: Fiber Orientation and Tissue Regeneration,” J. Theor. Biol., 199(4), pp. 449–471.
Dallon,  J., Sherratt,  J., Maini,  P., and Ferguson,  M., 2000, “Biological Implications of a Discrete Mathematical Model for Collagen Deposition and Alignment in Dermal Wound Repair,” IMA J. Math. Appl. Med. Biol., 17(4), pp. 379–393.
Olsen,  L., Maini,  P. K., Sherratt,  J. A., and Dallon,  J. C., 1999, “Mathematical Modelling of Anisotropy in Fibrous Connective Tissue,” Math. Biosci., 158(2), pp. 145–170.
Barocas,  V. H., and Tranquillo,  R. T., 1997, “An Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics: The Interplay Among Cell Traction, Fibrillar Network Deformation, Fibril Alignment and Cell Contact Guidance,” J. Biomech. Eng., 119(2), pp. 137–145.
Barocas,  V. H., and Tranquillo,  R. T., 1997, “A Finite Element Solution for the Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics: The Effect of Contact Guidance on Isometric Cell Traction Measurement,” J. Biomech. Eng., 119(3), pp. 261–268.
van Oijen, C. H. G. A., van de Vosse, F. N., and Baaijens, F. P. T., 2002, “An Updated Lagrange Formulation of A Constitutive Model for Incompressible Composite Materials at Finite Strains,” submitted to Computer Methods in Applied Mechanics and Engineering.
Carew,  E. O., Barber,  J. E., and Vesely,  I., 2000, “Role of Preconditioning and Recovery Time in Repeated Testing of Aortic Valve Tissues: Validation Through Quasilinear Viscoelastic Theory,” Ann. Biomed. Eng., 28(9), pp. 1093–1100.
Billiar,  K. L., and Sacks,  M. S., 2000, “Biaxial Mechanical Properties of the Natural and Glutaraldehyde Treated Aortic Valve Cusp—Part II: A Structural Constitutive Model,” J. Biomech. Eng., 122(4), pp. 327–335.
Bathe, K. J., 1996, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ.
Segal, A., 1984, SEPRAN User Manual, Standard Problems and Programmers Guide, Ingenieursbureau SEPRA, Leidschendam, the Netherlands.
MacKenna,  D., Summerour,  S. R., and Villarreal,  F. J., 2000, “Role of Mechanical Factors in Modulating Cardiac Fibroblast Function and Extracellular Matrix Synthesis,” Cardiovasc. Res., 46(2), pp. 257–263.
Kolpakov,  V., Rekhter,  M. D., Gordon,  D., Wang,  W. H., and Kulik,  T. J., 1995, “Effect of Mechanical Forces on Growth and Matrix Protein Synthesis in the in vitro Pulmonary Artery. Analysis of the Role of Individual Cell Types,” Circ. Res., 77(4), pp. 823–831.
Kim,  B. S., Nikolovski,  J., Bonadio,  J., and Mooney,  D. J., 1999, “Cyclic Mechanical Strain Regulates the Development of Engineered Smooth Muscle Tissue,” Nat. Biotechnol., 17(10), pp. 979–983.
Torbet,  J., and Ronzière,  M. C., 1984, “Magnetic Alignment of Collagen During Self-Assembly,” Biochem. J., 219(3), pp. 1057–1059.
Dubey,  N., Letourneau,  P. C., and Tranquillo,  R. T., 2001, “Neuronal Contact Guidance in Magnetically Aligned Fibrin Gels: Effect of Variation in Gel Mechano-Structural Properties,” Biomaterials, 22(10), pp. 1065–1075.
Streuli,  C., 1999, “Extracellular Matrix Remodelling and Cellular Differentiation,” Curr. Opin. Cell Biol., 11(5), pp. 634–640.
Thubrikar, M. J., 1990, The Aortic Valve, CRC Press, Boca Raton.
Vesely,  I., and Noseworthy,  R., 1992, “Micromechanics of the Fibrosa and the Ventricularis in Aortic Valve Leaflets,” J. Biomech., 25(1), pp. 101–113.
Thubrikar,  M. J., Aouad,  J., and Nolan,  S. P., 1986, “Comparison of the in vivo and in vitro Mechanical Properties of Aortic Valve Leaflets,” J. Thorac. Cardiovasc. Surg., 92(1), pp. 29–36.
de Hart, J., 2002, “Fluid-Structure Interaction in the Aortic Heart Valve: A Three-Dimensional Computational Analysis,” Ph.D. thesis, Technische Universiteit Eindhoven.
Clark,  R. E., and Finké,  E. H., 1974, “Scanning and Light Microscopy of Human Aortic Leaflets in Stressed and Relaxed States,” J. Thorac. Cardiovasc. Surg., 67(5), pp. 792–804.
Sacks,  M. S., Smith,  D. B., and Hiester,  E. D., 1997, “A Small Angle Light Scattering Device for Planar Connective Tissue Microstructural Analysis,” Ann. Biomed. Eng., 25(4), pp. 678–689.
Billiar,  K. L., and Sacks,  M. S., 2000, “Biaxial Mechanical Properties of the Natural and Glutaraldehyde Treated Aortic Valve Cusp—Part I: Experimental Results,” J. Biomech. Eng., 122(1), pp. 23–30.
Billiar,  K. L., and Sacks,  M. S., 1997, “A Method to Quantify Fiber Kinematics of Planar Tissues Under Biaxial Stretch,” J. Biomech., 30(7), pp. 753–756.
Scott,  M. J., and Vesely,  I., 1995, “Aortic Valve Cusp Microstructure: The Role of Elastin,” Ann. Thorac. Surg., 60(2), pp. S391–S394.
Scott,  M. J., and Vesely,  I., 1996, “Morphology of Porcine Aortic Valve Cusp Elastin,” J. Heart Valve Dis., 5(5), pp. 464–471.
Lee,  T. C., Midura,  R. J., Hascall,  V. C., and Vesely,  I., 2001, “The Effect of Elastin Damage on the Mechanics of the Aortic Valve,” J. Biomech., 34(2), pp. 203–210.
de Hart,  J., Peters,  G. W. M., Schreurs,  P. J. G., and Baaijens,  F. P. T., 2000, “A Two-Dimensional Fluid-Structure Interaction Model of the Aortic Valve,” J. Biomech., 33(9), pp. 1079–1088.
Vesely,  I., 1996, “Reconstruction of Loads in the Fibrosa and Ventricularis of Porcine Aortic Valves,” ASAIO J., 42(5), pp. M739–M746.
Carver,  W., Nagpal,  M. L., Nachtigal,  M., Borg,  T. K., and Terracio,  L., 1991, “Collagen Expression in Mechanically Stimulated Cardiac Fibroblasts,” Circ. Res., 69(1), pp. 116–122.
Lee,  A. A., Delhaas,  T., McCulloch,  A. D., and Villarreal,  F. J., 1999, “Differential Responses of Adult Cardiac Fibroblasts to in vitro Biaxial Strain Patterns,” J. Mol. Cell. Cardiol., 31(10), pp. 1833–1843.
Villarreal,  F. J., and Dillmann,  W. H., 1992, “Cardiac Hypertrophy-Induced Changes in mRNA Levels for TGF-Beta 1, Fibronectin, and Collagen,” Am. J. Physiol., 262(6), pp. H1861–H1866.
Doillon,  C. J., Dunn,  M. G., Bender,  E., and Silver,  F. H., 1985, “Collagen Fiber Formation in Repair Tissue: Development of Strength and Toughness,” Coll. Relat. Res., 5(6), pp. 481–492.


Grahic Jump Location
Fiber architecture in the native aortic heart valve leaflet (from 5 with permission). The fibers are mainly oriented along the circumferential direction and some radially oriented fibers are present at the base.
Grahic Jump Location
Schematic representation of fiber reorientation. The fiber (e⃗fj) is rotated over an angle Δθj towards the principal strain direction (e⃗pj), resulting in the new fiber direction (e⃗fj′).αj denotes the angle between e⃗fj and e⃗pj.
Grahic Jump Location
Schematic representation of the procedure to update the fiber directions in the undeformed configuration. The old fiber direction in the undeformed configuration (e⃗f0) is transformed to the fiber direction in the deformed configuration (e⃗f). The fiber direction is then rotated towards the principal strain direction to obtain the new fiber direction (e⃗f). Finally, back transformation results in the updated fiber direction in the undeformed configuration (e⃗f0).
Grahic Jump Location
Finite-element meshes of the valve in a stented (a) and stentless (b) geometry. In (b), the rigid stent from (a) is replaced by the aortic root and one sinus is omitted for an improved perspective. Because of symmetry only 16 of the valve was used in the finite-element analyses.
Grahic Jump Location
Tip displacements as a function of the relative period of time at different pressure levels (a, entries I, II, and III from Table 1), with different fiber stiffnesses (b, entries III, IV, and V from Table 1), different initial fiber directions (c, entries III and VI from Table 1), and different magnitudes of the rate constants (d, entries III, VII, VIII, and IX from Table 1).
Grahic Jump Location
Fiber configurations. Mean value of the final total volume fraction on the aortic and ventricular side (left). The color bar is subdivided into 10 discrete levels and the upper limit is set to 0.25, although in (a) maximum values of 0.3 are observed at the fixed edge. This truncation is performed to obtain a better resolution. Final fiber orientation on the aortic side of the leaflet (right). The fiber vectors are scaled with their volume fraction. (a) and (b) are obtained with reference values of the parameters (entry III in Table 1). (c) and (d) are obtained with a stentless valve geometry (entry X in Table 1). (e) and (f) are obtained with a stentless opened valve configuration (entry XI in Table 1).
Grahic Jump Location
Experimental data (left) of a fixed porcine aortic valve leaflet (from 35 with permission) together with the computed (right) final fiber directions in a stented valve geometry [from Fig. 6(b)]. The vector plots indicate the preferred fiber direction, running from commissure to commissure. The color map indicates the orientation index OI [deg], which is indicative for the degree of alignment. Highly aligned networks have low OI values, whereas more randomly oriented networks have larger values.




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