The annulus fibrosus plays a central role in biomechanical properties of the intervertebral disc; its collagen fibers span the vertebral bodies above and below it, serving to contain nuclear pressure, guide spinal motion, and allow flexibility. The nonlinear, anisotropic material properties of the annulus are largely defined by its highly organized collagenous architecture that can be compared to an angle-ply composite. A particularly useful annular constitutive model would reflect the structure of the annulus in the mathematical formulation. To this end, a strain energy function with separate terms to represent the matrix, the fibers, and the interactions between the constituents has been developed in the research described in this dissertation. Additionally, the tensile and compressive stress-strain response of the annulus in the circumferential direction and the tensile stress-strain response of the annulus in the axial direction both before and after the test specimens have been incubated in a glycadon solution are reported. Using nonlinear regression, the strain energy function is simultaneously applied to these new data and to data from a wide range of experimental protocols reported in the literature to determine values for the material coefficients appearing in the constitutive equation.
It is determined that the elastic modulus of the annulus is essentially continuous through the point of zero strain in the circumferential direction. By choosing experimental protocols that all use a nearly stress-free reference configuration, a comprehensive formulation for the multiaxial annular elastic behavior is developed. Non-enzymatic collagen crosslinking is shown to induce a statistically significant change in the material properties of the annulus in the axial direction. Furthermore, the collagen crosslink density is shown to correlate positively only with the material coefficients of the interactions terms in the strain energy function. As a validation, the strain energy function is extrapolated to predict the results from an experimental protocol that had not been included in the nonlinear regression. In the future, this mechanistic constitutive relationship may be used to correlate specific features of tissue architecture to material properties, providing further insight into the structure-function relationships of the annulus fibrosus.
|1998||Reihsner R, Menzel EJ. Two-dimensional stress-relaxation behavior of human skin as influenced by non-enzymatic glycation and the inhibitory agent aminoguanidine. J Biomech. November 1998;31(11):985-993.|
|1996||Weiss JA, Maker BN, Govindjee S. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Meth Appl Mech Eng. August 15, 1996;135(1-2):107-128.|
|1989||Cassidy JJ, Hiltner A, Baer E. Hierarchical structure of the intervertebral disc. Connect Tissue Res. 1989;23(1):75-88.|
|1989||Sell DR, Monnier VM. Structure elucidation of a senescence cross-link from human extracellular matrix: implication of pentoses in the aging process. J Biol Chem. December 25, 1989;264(36):21597-21602.|
|1990||White AA III, Panjabi MM. Clinical Biomechanics of the Spine. 2nd ed. Philadelphia, PA: J.B. Lippincott Company; 1990.|
|2000||Holzapfel GA, Gasser TC, Ogden RW. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast. 2000;61(1-3):1-48.|
|1999||Bass EC. Biaxial Nonlinear Elastic Response of the Human Lumbar Annulus Fibrosus and Its Role in the Determination of a Physiologically Relevant Constitutive Relation [PhD thesis]. Berkeley, CA: Berkeley, University of California; 1999.|
|1993||Fung YC. Biomechanics: Mechanical Properties of Living Tissues. 2nd ed. New York, NY: Springer-Verlag; 1993.|
|1979||Fung YC, Fronek K, Patitucci P. Pseudoelasticity of arteries and of its mathematical expression. Am J Physiol. 1979;237(5):H620-H631.|
|1998||Quapp KM, Weiss JA. Material characterization of human medial collateral ligament. J Biomech Eng. 1998;120(6):757-763.|
|1990||Thompson JP, Pearce RH, Schechter MT, Adams ME, Tsang IK, Bishop PB. Preliminary evaluation of a scheme for grading the gross morphology of the human intervertebral disc. Spine. May 1990;15(5):411-415.|
|1994||Skaggs DL, Weidenbaum M, Iatridis JC, Ratcliffe A, Mow VC. Regional variation in tensile properties and biochemical composition of the human lumbar anulus fibrosus. Spine. June 1994;19(12):1310-1319.|
|1967||Fung YCB. Elasticity of soft tissues in simple elongation. Am J Physiol. December 1967;213(6):1532-1544.|
|1984||Eyre DR, Paz MA, Gallop PM. Cross-linking in collagen and elastin. Ann Rev Biochem. 1984;53:717-748.|