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Geometrical aspects of patient-specific modelling of the intervertebral disc: collagen fibre orientation and residual stress distribution

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Abstract

Patient-specific modelling of the spine is a powerful tool to explore the prevention and the treatment of injuries and pathologies. Albeit several methods have been proposed for the discretization of the bony structures, the efficient representation of the intervertebral disc anisotropy remains a challenge, especially with complex geometries. Furthermore, the swelling of the disc’s nucleus pulposus is normally added to the model after geometry definition, at the cost of changes of the material properties and an unrealistic description of the prestressed state. The aim of this study was to develop techniques, which preserve the patient-specific geometry of the disc and allow the representation of the system anisotropy and residual stresses, independent of the system discretization. Depending on the modelling features, the developed approaches resulted in a response of patient-specific models that was in good agreement with the physiological response observed in corresponding experiments. The proposed methods represent a first step towards the development of patient-specific models of the disc which respect both the geometry and the mechanical properties of the specific disc.

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References

  • Acaroglu ER, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M (1995) Degeneration and aging affect the tensile behavior of human lumbar anulus fibrosus. Spine 20:2690–2701

    Article  Google Scholar 

  • Andersson GBJ, Schultz AB (1979) Effects of fluid injection on mechanical properties of intervertebral discs. J Biomech 12:453–458

    Article  Google Scholar 

  • Antoniou J, Steffen T, Nelson F, Winterbottom N, Hollander AP, Poole RA, Aebi M, Alini M (1996) The human lumbar intervertebral disc: evidence for changes in the biosynthesis and denaturation of the extracellular matrix with growth, maturation, ageing, and degeneration. J Clin Invest 98:996–1003

    Article  Google Scholar 

  • Bass EC, Ashford FA, Segal MR, Lotz JC (2004) Biaxial testing of human annulus fibrosus and its implications for a constitutive formulation. Ann Biomed Eng 32:1231–1242

    Article  Google Scholar 

  • Breau C, Shirazi-Adl A, de Guise J (1991) Reconstruction of a human ligamentous lumbar spine using ct images: a three dimensional finite element mesh generation. Ann Biomed Eng 19:291–302

    Article  Google Scholar 

  • Brickley-Parsons D, Glimcher MJ (1984) Is the chemistry of collagen in intervertebral discs an expression of Wolff’s law? a study of the human lumbar spine. Spine 9:148–163

    Article  Google Scholar 

  • Cassidy JJ, Hiltner A, Baer E (1989) Hierarchical structure of the intervertebral disc. Connect Tissue Res 23:75–88

    Article  Google Scholar 

  • Charlebois M, Pretterklieber M, Zysset PK (2010) The role of fabric in the large strain compressive behavior of human trabecular bone. J Biomech Eng 132(121):006

    Google Scholar 

  • Cloyd JM, Malhotra NR, Weng L, Chen W, Mauck RL, Elliott DM (2007) Material properties in unconfined compression of human nucleus pulposus, injectable hyaluronic acid-base hydrogels and tissue engineering scaffolds. Eur Spine J 16:1892–1898

    Article  Google Scholar 

  • Dreischarf M, Rohlmann A, Zhu R, Schmidt H, Zander T (2013) Is it possible to estimate the compressive force in the lumbar spine from intradiscal pressure measurements? A finite element evaluation. Med Eng Phys 35:1385–1390

    Article  Google Scholar 

  • Du C, Mo Z, Tian S, Wang L, Fan J, Liu S, Fan Y (2014) Biomechanical investigation of thoracolumbar spine in different postures during ejection using a combined finite element and multi-body approach. Int J Numer Method Biomed Eng 30:1121–1131

    Article  Google Scholar 

  • Eberlein R, Holzapfel GA, Schulze-Bauer CA (2001) An anisotropic model for annulus tissue and enhanced finite element analyses of intact lumbar disc bodies. Comput Methods Biomech Biomed Eng 4:209–229

    Article  Google Scholar 

  • Ehlers W, Karajan N, Markert B (2006) A porous media model describing the inhomogeneous behaviour of the human intervertebral disc. Materialwiss Werkstofftech 37:546–551

    Article  Google Scholar 

  • Ehlers W, Karajan N, Markert B (2009) An extended biphasic model for charged hydrated tissues with application to the intervertebral disc. Biomech Model Mechanobiol 8:233–251

    Article  Google Scholar 

  • El-Rich M, Arnoux PJ, Wagnac E, Brunet C, Aubin CE (2009) Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions. J Biomech 42:1252–1262

    Article  Google Scholar 

  • Ezquerro F, Vacas FG, Postigo SMP, Simón A (2011) Calibration of the finite element model of a lumbar functional spinal unit using an optimization technique based on differential evolution. Med Eng Phys 33:89–95

    Article  Google Scholar 

  • Fagan MJ, Julian S, Siddall DJ, Mohsen AM (2002) Patient-specific spine models—part 1: finite element analysis of the lumbar intervertebral disc: a material sensitivity study. Proc Inst Mech Eng H J Eng Med 216:299–314

    Article  Google Scholar 

  • Ferguson SJ, Ito K, Nolte LP (2004) Fluid flow and convective transport of solutes within the intervertebral disc. J Biomech 37:213–221

    Article  Google Scholar 

  • Fujita Y, Duncan NA, Lotz JC (1997) Radial tensile properties of the lumbar annulus fibrosus are site and degeneration dependent. J Orthop Res 15:814–819

    Article  Google Scholar 

  • Galbusera F, Schmidt H, Noailly J, Malandrino A, Lacroix D, Wilke HJ, Shirazi-Adl A (2011) Comparison of four methods to simulate swelling in poroelastic finite element models of intervertebral discs. J Mech Behav Biomed Mater 4:1234–1241

    Article  Google Scholar 

  • Gardiner JC, Weiss JA (2003) Subject-specific finite element analysis of the human medial collateral ligament during valgus knee loading. J Orthop Res 21:1098–1106

    Article  Google Scholar 

  • Goel VK, Monroe BT, Gilbertson L, Brinckmann P (1995) Interlaminar shear stresses and laminae separation in a disc. Spine 20:689–698

    Article  Google Scholar 

  • Grosland N, Goel VK (2007) Vertebral endplate morphology follows bone remodeling principles. Spine 32:E667–E673

    Article  Google Scholar 

  • Haut RC, Little RW (1972) A constitutive equation for collagen fibers. J Biomech 5:423–430

    Article  Google Scholar 

  • Herbert CM, Lindberg KA, Jayson MI, Bailey AJ (1975) Changes in the collagen of human intervertebral discs during ageing and degenerative disc disease. J Mol Med 1:79–91

    Google Scholar 

  • Heuer F, Schmidt H, Klezl Z, Claes L, Wilke HJ (2007a) Stepwise reduction of functional spinal structures increase range of motion and change lordosis angle. J Biomech 40:271–280

    Article  Google Scholar 

  • Heuer F, Schmidt H, Claes L, Wilke HJ (2007b) Stepwise reduction of functional spinal structures increase vertebral translation and intradiscal pressure. J Biomech 40:795–803

    Article  Google Scholar 

  • Holzapfel GA, Schulze-Bauer CA, Feigl G, Regitnig P (2005) Single lamellar mechanics of the human lumbar anulus fibrosus. Biomech Model Mechanobiol 3:125–140

    Article  Google Scholar 

  • Hsu EW, Setton LA (1999) Diffusion tensor microscopy of the intervertebral disc anulus fibrosus. Magn Reson Med 41:992–999

    Article  Google Scholar 

  • Iatridis JC, Weidenbaum M, Setton LA, Mow VC (1996) Is the nucleus pulposus a solid or a fluid? mechanical behaviors of the nucleus pulposus of the human intervertebral disc. Spine 21:1174– 1184

    Article  Google Scholar 

  • Iatridis JC, Laible JL, Krag MH (2003) Influence of fixed charge density magnitude and distribution on the intervertebral disc: applications of a poroelastic and chemical electric (PEACE) model. J Biomech Eng 125:12–24

    Article  Google Scholar 

  • Iatridis JC, MacLean JJ, O’Brien M, Stokes IA (2007) Measurements of proteoglycans and water content distribution in human lumbar intervertebral discs. Spine 32:1493–1497

    Article  Google Scholar 

  • Jacobs NT, Cortes DH, Peloquin JM, Vresilovic EJ, Elliott DM (2014) Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent. J Biomech 47:2540–2546

    Article  Google Scholar 

  • Johannessen W, Elliott DM (2005) Effects of degeneration on the biphasic material properties of human nucleus pulposus in confined compression. Spine 30:E724–E729

    Article  Google Scholar 

  • Kasra LE (1975) Creep characteristics of the human spinal column. Orthop Clin N Am 6:3–18

    Google Scholar 

  • Koeller W, Muehlhaus S, Meier W, Hartmann F (1986) Biomechanical properties of human intervertebral discs subjected to axial dynamic compression-influence of age and degeneration. J Biomech 19:807–816

    Article  Google Scholar 

  • Koh I, Marini G, Vogt PJ, Ferguson SJ (2013) Investigating the effect of vertebroplasty on complex vertebral fractures. In: Proceedings of 5th international conference computational bioengineering, ICCB2013, Leuven, Belgium

  • Kurtz SM, Avram E (2006) Spine technology handbook. Academic Press, Burlington, MA

    Google Scholar 

  • Li G, Wang S, Passias P, Xia Q, Li G, Wood K (2009) Segmental in vivo vertebral motion during functional human lumbar spine activities. Eur Spine J 18:1013–1021

    Article  Google Scholar 

  • Little JP, Adam CJ, Evans JH, Pettet GJ, Pearcy MJ (2007) Nonlinear finite element analysis of anular lesions in the L4/5 intervertebral disc. J Biomech 40:2744–2751

    Article  Google Scholar 

  • Lu Y, Maquer G, Museyko O, Püschel K, Engelke K, Zysset P, Morlock M, Huber G (2014) Finite element analyses of human vertebral bodies embedded in polymethylmethalcrylate or loaded via the hyperelastic intervertebral disc models provide equivalent predictions of experimental strength. J Biomech 47:2512–2516

    Article  Google Scholar 

  • Malandrino A, Noailly J, Lacroix D (2013) Regional annulus fibre orientations used as a tool for the calibration of lumbar intervertebral disc finite element models. Comput Methods Biomech Biomed Eng 16:923–928

    Article  Google Scholar 

  • Marchand F, Ahmed AM (1990) Investigation of the laminate structure of lumbar disc anulus fibrosus. Spine 15:402–410

    Article  Google Scholar 

  • Marini G, Ferguson SJ (2014a) Modelling the influence of heterogeneous annulus material property distribution on intervertebral disc mechanics. Ann Biomed Eng 42:1760–1772

    Article  Google Scholar 

  • Marini G, Ferguson SJ (2014b) Nonlinear numerical analysis of the structural response of the intervertebral disc to impact loading. Comput Methods Biomech Biomed Eng 17:1002–1011

    Article  Google Scholar 

  • Marini G, Koh I, Studer H, Ferguson SJ (2012) An algorithm for modelling the fibre distribution of the annulus fibrosus within arbitrarily-aligned meshes. In: Proceedings of 10th international symposium on computer methods in biomechanics and biomedical engineering, CMBBE2012, Berlin

  • Marini G, Huber G, Püschel K, Ferguson SJ (2015) Nonlinear dynamics of the human lumbar intervertebral disc. J Biomech 48:479–488

    Article  Google Scholar 

  • McNally DS, Adams MA (1992) Internal intervertebral disc mechanics as revealed by stress profilometry. Spine 17:66–73

    Article  Google Scholar 

  • Mengoni M, Luxmoore BJ, Wijayathunga VN, Jones AC, Broom ND, Wilcox RK (2015) Derivation of inter-lamellar behaviour of the intervertebral disc annulus. J Mech Behav Biomed Mater 48:164–172

    Article  Google Scholar 

  • Moramarco V, Palomar APD, Pappalettere C, Doblare M (2010) An accurate validation of a computational model of a human lumbosacral segment. J Biomech 43:334–342

    Article  Google Scholar 

  • Mukherjee P, Chung SW, Berman JI, Hess CP, Henry RG (2008) Diffusion tensor mr imaging and fiber tractography: technical considerations. Am J Neuroradiol 29:843–852

    Article  Google Scholar 

  • Nachemson A, Morris JM (1964) In vivo measurements of intradiscal pressure: discometry, a method for the determination of pressure in the lower lumbar discs. J Bone Joint Surg 46:1077–1092

    Google Scholar 

  • Noailly J, Planell JA, Lacroix D (2011) On the collagen criss-cross angles in the annuli fibrosis of lumbar spine finite element models. Biomech Model Mechanobiol 10:203–219

    Article  Google Scholar 

  • O’Connell GD, Vresilovic EJ, Elliott DM (2007) Comparison of animals used in disc research to human lumbar disc geometry. Spine 32:328–333

    Article  Google Scholar 

  • O’Connell GD, Sen S, Elliott DM (2012) Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration. Biomech Model Mechanobiol 11:493–503

    Article  Google Scholar 

  • Onate E (2009) Structural analysis with the finite element method: linear statics. Springer, Netherlands

    Book  MATH  Google Scholar 

  • Panjabi MM (1992) The stabilizing system of the spine—part II: neutral zone and instability hypothesis. J Spinal Disord 5:390–397

    Article  Google Scholar 

  • Peloquin JM, Yoder JH, Jacobs NT, Moon SM, Wright AC, Vresilovic EJ, Elliott DM (2014) Human L3L4 intervertebral disc mean 3D shape, modes of variation, and their relationship to degeneration. J Biomech 47:2452–2459

    Article  Google Scholar 

  • Pena E, Martinez MA, Calvo B, Doblaré M (2006) On the numerical treatment of initial strains in biological soft tissues. Int J Numer Meth Eng 68:836–860

    Article  MATH  Google Scholar 

  • Perie DS, Maclean JJ, Owen J, Iatridis J (2006) Correlating material properties with tissue composition in enzymatically digested bovine annulus fibrosus and nucleus pulposus tissue. Ann Biomed Eng 34:769–777

    Article  Google Scholar 

  • Pezowicz CA, Robertson PA, Broom ND (2006) The structural basis of interlamellar cohesion in the intervertebral disc wall. J Anat 208:317–330

    Article  Google Scholar 

  • Pfirrmann CWA, Metzdorf A, Zanetti M, Hodler J, Boos N (2001) Magnetic resonance classification of lumbar intervertebral disc degeneration. Spine 26:1873–1878

    Article  Google Scholar 

  • Reutlinger C, Bürki A, Brandejsky V, Ebert L, Büchler P (2014) Specimen specific parameter identification of ovine lumbar intervertebral discs: on the influence of fibre-matrix and fibre-fibre shear interactions. J Mech Behav Biomed Mater 30:279–289

    Article  Google Scholar 

  • Riveros F, Chandra S, Finol EA, Gasser TC, Rodriguez JF (2013) A pull-back algorithm to determine the unloaded vascular geometry in anisotropic hyperelastic AAA passive mechanics. Ann Biomed Eng 41:694–708

    Article  Google Scholar 

  • Schmidt H, Heuer F, Wilke HJ (2009) Which axial and bending stiffnesses of posterior implants are required to design a flexible lumbar stabilisation system. J Biomech 42:48–54

    Article  Google Scholar 

  • Schmidt H, Galbusera F, Rohlmann A, Shirazi-Adl A (2013) What have we learned from finite element model studies of lumbar intervertebral discs in the past four decades? J Biomech 46:2342–2355

    Article  Google Scholar 

  • Schroeder Y, Wilson W, Huyghe JM, Baaijens FP (2006) Osmoviscoelastic finite element model of the intervertebral disc. Eur Spine J 15:361–371

    Article  Google Scholar 

  • Shirazi-Adl A, Ahmed AM, Shrivastava SC (1986) Mechanical response of a lumbar motion segment in axial torque alone and combined with compression. Spine 11:914–927

    Article  Google Scholar 

  • Studer HP, Larrea X, Riedwyl H, BÃijchler P (2010) Biomechanical model of human cornea based on stromal microstructure. J Biomech 43:836–842

    Article  Google Scholar 

  • Studer HP, Riedwyl H, Amstutz CA, Hanson JVM, Büchler P (2013) Patient-specific finite-element simulation of the human cornea: a clinical validation study on cataract surgery. J Biomech 46:751–758

    Article  Google Scholar 

  • Teo EC, Lee KK, Qiu TX, Ng HW, Yang K (2004) The biomechanics of lumbar graded facetectomy under anterior-shear load. IEEE Trans Biomed Eng 51:443–449

    Article  Google Scholar 

  • Thompson JP, Pearce RH, Schechter MT, Adams ME, Tsang IKY, Bishop PB (1990) Preliminary evaluation of a scheme for grading the gross morphology of the human intervertebral disc. Spine 15:411–415

    Article  Google Scholar 

  • Twomey L, Taylor J (1985) Age changes in lumbar intervertebral discs. Acta Orthop Scand 56:496–499

  • Urban JPG, Maroudas A (1981) Swelling of the intervertebral disc in vitro. Connect Tissue Res 25:1–10

    Article  Google Scholar 

  • Urban JPG, McMullin JF (1988) Swelling pressure of the lumbar intervertebral discs: influence of age, spinal level, composition, and degeneration. Spine 13:179–186

    Article  Google Scholar 

  • Vignollet J (2012) Computational strategies toward the modelling of the intervertebral disc. Doctoral dissertation, University of Glasgow

  • Wang SP, Gadikota HR, Miao J, Kim YH, Wood KB, Li G (2013) A combined numerical and experimental technique for estimation of the forces and moments in the lumbar intervertebral disc. Comput Methods Biomech Biomed Eng 16:1278–1286

    Article  Google Scholar 

  • Weisse B, Aiyangar AK, Affolter C, Gander R, Terrasi GP, Ploeg H (2012) Determination of the translational and rotational stiffnesses of an L4–L5 functional spinal unit using a specimen-specific finite element model. J Mech Behav Biomed Mater 13:45–61

    Article  Google Scholar 

  • White AAI, Panjabi MM (1978) Clinical biomechanics of the spine. Lippincott Williams & Wilkins Company J.B, Philadelphia

    Google Scholar 

  • Wilke HJ, Neef P, Caimi M, Hoogland T, Claes LE (1999) New in vivo measurements of pressures in the intervertebral disc in daily life. Spine 24:755–762

    Article  Google Scholar 

  • Wilson W, van Donkelaar CC, Huyghe JM (2005) A comparison between mechano-electrochemical and biphasic swelling theories for soft hydrated tissues. J Biomech Eng 127:158–165

    Article  Google Scholar 

  • Yamada H (1970) Strength of biological material. Williams & Wilkins, Baltimore, Maryland

    Google Scholar 

  • Yushkevich PA, Piven J, Hazlett HC, Smith RG, Ho S, Gee JC, Gerig G (2006) User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. Neuroimage 31:1116–1128

    Article  Google Scholar 

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Acknowledgments

Funding for this research project was provided by the European Union through a Marie Curie action (FPT7-PITN-GA-2009-238690-SPINEFX).

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Authors and Affiliations

  1. Institute for Biomechanics, ETH Zurich, Zurich, Switzerland

    Giacomo Marini & Stephen J. Ferguson

  2. Integrated Scientific Service AG, Biel, Switzerland

    Harald Studer

  3. Institute of Biomechanics, TUHH Hamburg University of Technology, Hamburg, Germany

    Gerd Huber

  4. Institute for Forensic Medicine, University Medical Center Hamburg-Eppendorf, Hamburg, Germany

    Klaus Püschel

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  1. Giacomo Marini
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  2. Harald Studer
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  4. Klaus Püschel
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  5. Stephen J. Ferguson
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Correspondence to Giacomo Marini.

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Marini, G., Studer, H., Huber, G. et al. Geometrical aspects of patient-specific modelling of the intervertebral disc: collagen fibre orientation and residual stress distribution. Biomech Model Mechanobiol 15, 543–560 (2016). https://doi.org/10.1007/s10237-015-0709-6

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