Tensile Properties of Nondegenerate Human Lumbar Anulus Fibrosus

Abstract

The observed variations in tensile behavior of multiple-layer anulus samples indicate that larger variations in tensile modulus and failure properties occur with radial position in the disc than from anterior to posterolateral regions. This pattern is likely related to site-specific variations in the tensile properties of the single-layer samples of anulus fibrosus lamellae and the organization of successive lamellae and their interactions. The results of the present study suggest that factors other than age, such as compositional and structural variations in the disc, are the most important determinants of tensile behavior of the anulus fibrosus.

Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus

“…The predicted stress}stretch relations remained convex to stretches of 0.3 in the con"ned compression protocols, which would be the maximum allowed stretch based on an initial solid content of 0.3 (Best et al, 1994) and the biphasic constraint of intrinsic incompressibility (Holmes and Mow, 1990). In addition, convexity was predicted in tensile tests beyond the reported failure stretches of 1.8 for a radial tension protocol (Fujita et al, 1997) and 1.15 for a circumferential tension protocol (Ebara et al, 1996). Since strict convexity is a su$cient condition for in cremental stability and uniqueness (Ogden, 1997), we regard the proposed strain energy function (11), along with the reported material constants, as being physically plausible for the range of deformations studied.…”

“…(11), the best-"t values of (� , � , � , � , � , � , � , � , � ) � � � � � � � � �� were (0.001, !0.737, !3.289, !6.496, 0.4091, 17.713, � � � � � � � � � �� �� resulted in a �� value of 0.35. A"radial con"ned compression (Iatridis et al, 1998); B"axial con"ned compression (Iatridis et al, 1998); C"radial tension (Fujita et al, 1997); D"circumferential tension (Ebara et al, 1996). Solid curves"mean experimental response $1 standard deviation; open circles"theoretical prediction of measured stress}stretch response.…”

“…A few constitutive inequalities which have been proposed in the past include the Baker}Ericksen inequalities, convexity, � � � � � � � � �� A"radial con"ned compression (Iatridis et al, 1998); B"axial con"ned compression (Iatridis et al, 1998); C"radial tension (Fujita et al, 1997); D"circumferential tension (Ebara et al, 1996). Solid curves"mean experimental response $1 standard deviation; open circles"theoretical prediction of measured stress}stretch response; "lled squares"theoretical prediction of &traction-free' stress}stretch response for experiments C and D.…”

“…The experimental data to which we applied the strain energy functions (9) and (11) included: (A) con"ned com pression, radial stress vs. radial stretch, nondegenerate anterior outer (Iatridis et al, 1998); (B) con"ned compres sion, axial stress vs. axial stretch, nondegenerate anterior outer (Iatridis et al, 1998); (C) simple tension, radial stress vs. radial stretch, nondegenerate anterior middle (Fujita et al, 1998); (D) simple tension, circumferential stress vs. circumferential stretch, nondegenerate anterior outer and inner (Ebara et al, 1996) (Fig. 2).…”

“…The continuum approach may be prefer able since the tissue properties could be de"ned directly by experimental data, as compared to the composite approach where the behavior of the individual constitu ents are needed but cannot be determined explicitly. Previous attempts at using the continuum approach were limited by: (1) the assumption of incompressibility (Wu and Yao, 1976) (annular tissue is now known to posses signi"cant compressibility (Iatridis et al, 1998)); (2) as sumption of linearity (Elliott et al, 1997) (the annulus demonstrates signi"cant nonlinearity under physiologic loads (Shirazi-Adl et al, 1986)); and (3) the use of data from only a single type of experiment (Galante, 1967;Fujita et al, 1997;Ebara et al, 1996;Iatridis et al, 1998). The objective of this study was to develop a nonlinear, orthotropic constitutive law for the solid phase of the annulus "brosus that, in the future, could be used to provide accurate predictions of the in vivo stresses within disc tissue.…”