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Single lamellar mechanics of the human lumbar anulus fibrosus

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Abstract

The mechanical behavior of the entire anulus fibrosus is determined essentially by the tensile properties of its lamellae, their fiber orientations, and the regional variation of these quantities. Corresponding data are rare in the literature. The paper deals with an in vitro study of single lamellar anulus lamellae and aims to determine (i) their tensile response and regional variation, and (ii) the orientation of lamellar collagen fibers and their regional variation. Fresh human body-disc-body units (L1–L2, n=11) from cadavers were cut midsagittally producing two hemidisc units. One hemidisc was used for the preparation of single lamellar anulus specimens for tensile testing, while the other one was used for the investigation of the lamellar fiber orientation. Single lamellar anulus specimens with adjacent bone fragments were isolated from four anatomical regions: superficial and deep lamellae (3.9±0.21 mm, mean ± SD, apart from the outer boundary surface of the anulus fibrosus) at ventro-lateral and dorsal positions. The specimens underwent cyclic uniaxial tensile tests at three different strain rates in 0.15 mol/l NaCl solution at 37°C, whereby the lamellar fiber direction was aligned with the load axis. For the characterization of the tensile behavior three moduli were calculated: Elow (0–0.1 MPa), Emedium (0.1–0.5 MPa) and Ehigh (0.5–1 MPa). Additionally, specimens were tested with the load axis transverse to the fiber direction. From the second hemidisc fiber angles with respect to the horizontal plane were determined photogrammetrically from images taken at six circumferential positions from ventral to dorsal and at three depth levels. Tensile moduli along the fiber direction were in the range of 28–78 MPa (regional mean values). Superficial lamellae have larger Emedium (p=0.017) and Ehigh (p=0.012) than internal lamellae, and the mean value of superficial lamellae is about three times higher than that of deep lamellae. Tensile moduli of ventro-lateral lamellae do not differ significantly from the tensile moduli of dorsal lamellae, and Elow is generally indifferent with respect to the anatomical region. Tensile moduli transverse to the fiber direction were about two orders of magnitude smaller (0.22±0.2 MPa, mean ± SD, n=5). Tensile properties are not correlated significantly with donor age. Only small viscoelastic effects were observed. The regional variation of lamellar fiber angle ϕ is described appropriately by a regression line |ϕ|=23.2+0.130×α (r2=0.55, p<0.001), where α is the polar angle associated with the circumferential position. The single anulus lamella may be seen as the elementary structural unit of the anulus fibrosus, and exhibits marked anisotropy and distinct regional variation of tensile properties and fiber angles. These features must be considered for appropriate physical and numerical modeling of the anulus fibrosus.

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Acknowledgements

The authors are particularly indebted to Markus Fröhlich, Sulzer Medica (now Centerpulse Orthopedics Ltd.), Winterthur, Switzerland, for valuable contributions. We thank Professor Reinhold Reimann from the Institute of Anatomy, Medical University Graz, for helpful ideas and motivating comments, and Elisabeth Pernkopf and Christian Chiocirca for their help regarding the experimental and dissecting works. We also like to acknowledge Robert Eberlein, from Sulzer Markets and Technology Ltd., for valuable discussions. Financial support for this research was provided by Sulzer Medica (now Centerpulse Orthopedics Ltd.), which is gratefully acknowledged.

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Correspondence to G. A. Holzapfel.

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Holzapfel, G.A., Schulze-Bauer, C.A.J., Feigl, G. et al. Single lamellar mechanics of the human lumbar anulus fibrosus. Biomech Model Mechanobiol 3, 125–140 (2005). https://doi.org/10.1007/s10237-004-0053-8

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  • DOI: https://doi.org/10.1007/s10237-004-0053-8

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