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      A novel finite element model of the ovine lumbar intervertebral disc with anisotropic hyperelastic material properties

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          Abstract

          The Ovine spine is an accepted model to investigate the biomechanical behaviour of the human lumbar one. Indeed, the use of animal models for in vitro studies is necessary to investigate the mechanical behaviour of biological tissue, but needs to be reduced for ethical and social reasons. The aim of this study was to create a finite element model of the lumbar intervertebral disc of the sheep that may help to refine the understanding of parallel in vitro experiments and that can be used to predict when mechanical failure occurs. Anisotropic hyperelastic material properties were assigned to the annulus fibrosus and factorial optimization analyses were performed to find out the optimal parameters of the ground substance and of the collagen fibers. For the ground substance of the annulus fibrosus the investigation was based on experimental data taken from the literature, while for the collagen fibers tensile tests on annulus specimens were conducted. Flexibility analysis in flexion-extension, lateral bending and axial rotation were conducted. Different material properties for the anterior, lateral and posterior regions of the annulus were found. The posterior part resulted the stiffest region in compression whereas the anterior one the stiffest region in tension. Since the flexibility outcomes were in a good agreement with the literature data, we considered this model suitable to be used in conjunction with in vitro and in vivo tests to investigate the mechanical behaviour of the ovine lumbar disc.

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          Are animal models useful for studying human disc disorders/degeneration?

          Intervertebral disc (IVD) degeneration is an often investigated pathophysiological condition because of its implication in causing low back pain. As human material for such studies is difficult to obtain because of ethical and government regulatory restriction, animal tissue, organs and in vivo models have often been used for this purpose. However, there are many differences in cell population, tissue composition, disc and spine anatomy, development, physiology and mechanical properties, between animal species and human. Both naturally occurring and induced degenerative changes may differ significantly from those seen in humans. This paper reviews the many animal models developed for the study of IVD degeneration aetiopathogenesis and treatments thereof. In particular, the limitations and relevance of these models to the human condition are examined, and some general consensus guidelines are presented. Although animal models are invaluable to increase our understanding of disc biology, because of the differences between species, care must be taken when used to study human disc degeneration and much more effort is needed to facilitate research on human disc material.
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            Anatomy of the sheep spine and its comparison to the human spine.

            The sheep spine is often used as a model for the human spine, although the degree to which these spines are anatomically comparable has yet to be categorically established. The purpose of this study was to investigate the characteristic anatomical dimensions of the sheep spine and to compare these with existing human data. Five complete spines were measured to determine 21 dimensions from the pedicles, spinal canal, transverse and spinous processes, facets, endplates, and disc. The results showed that sheep and human vertebrae are most similar in the thoracic and lumbar regions, although they show substantial differences in certain dimensions. Morphological variations as a function of spine level typically were well matched in the two species. Sheep spine may be a useful model for experiments related to the gross structure of the thoracic or lumbar spine, with certain limitations for the cervical spine. A thorough database has been provided for deciding the appropriateness of using the sheep spine as a model for the human spine.
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              Single lamellar mechanics of the human lumbar anulus fibrosus.

              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 degrees C, whereby the lamellar fiber direction was aligned with the load axis. For the characterization of the tensile behavior three moduli were calculated: E(low) (0-0.1 MPa), E(medium) (0.1-0.5 MPa) and E(high) (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 E(medium) (p=0.017) and E(high) (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 E(low) 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 phi is described appropriately by a regression line |phi|=23.2 + 0.130 x alpha (r(2)=0.55, p<0.001), where alpha 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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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                4 May 2017
                2017
                : 12
                : 5
                : e0177088
                Affiliations
                [1 ]Laboratory of Biological Structure Mechanics (LaBS), Department of Chemistry, Materials and Chemical Engineering "Giulio Natta", Politecnico di Milano, Milan, Italy
                [2 ]IRCCS Istituto Ortopedico Galeazzi, Milan, Italy
                [3 ]Institute of Orthopaedic Research and Biomechanics, Center for Musculoskeletal Research (zmfu), Ulm University, Ulm, Germany
                University of Pennsylvania, UNITED STATES
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                • Conceptualization: GC FG HJW TV.

                • Data curation: GC FG RJ BS.

                • Formal analysis: GC FG.

                • Investigation: GC.

                • Methodology: GC FG TV.

                • Project administration: TV.

                • Resources: GC FG HJW TV.

                • Software: GC FG RJ BS.

                • Supervision: FG.

                • Validation: GC FG.

                • Visualization: GC.

                • Writing – original draft: GC FG TV.

                • Writing – review & editing: GC FG TV.

                Author information
                http://orcid.org/0000-0001-6084-9530
                Article
                PONE-D-16-35990
                10.1371/journal.pone.0177088
                5417645
                28472100
                2feb4ad6-b4d6-44c8-abd5-9cb3cd6bd720
                © 2017 Casaroli et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 15 September 2016
                : 21 April 2017
                Page count
                Figures: 10, Tables: 1, Pages: 18
                Funding
                The authors received no specific funding for this work.
                Categories
                Research Article
                Biology and Life Sciences
                Biochemistry
                Proteins
                Collagens
                Biology and Life Sciences
                Organisms
                Animals
                Vertebrates
                Amniotes
                Mammals
                Ruminants
                Sheep
                Physical Sciences
                Materials Science
                Materials by Structure
                Fibers
                Physical Sciences
                Physics
                Classical Mechanics
                Deformation
                Bending
                Physical Sciences
                Physics
                Classical Mechanics
                Damage Mechanics
                Deformation
                Bending
                Physical Sciences
                Materials Science
                Material Properties
                Physical Sciences
                Physics
                Classical Mechanics
                Mechanical Stress
                Physical Sciences
                Mathematics
                Applied Mathematics
                Finite Element Analysis
                Physical Sciences
                Physics
                Condensed Matter Physics
                Anisotropy
                Physical Sciences
                Materials Science
                Material Properties
                Anisotropy
                Custom metadata
                All relevant data are within the paper and its Supporting Information files.

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                Uncategorized

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