Skip to main content
Log in

Evaluation of nucleus pulposus fluid velocity and pressure alteration induced by cartilage endplate sclerosis using a poro-elastic finite element analysis

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

The nucleus pulposus (NP) in the intervertebral disk (IVD) depends on diffusive fluid transport for nutrients through the cartilage endplate (CEP). Disruption in fluid exchange of the NP is considered a cause of IVD degeneration. Furthermore, CEP calcification and sclerosis are hypothesized to restrict fluid flow between the NP and CEP by decreasing permeability and porosity of the CEP matrix. We performed a finite element analysis of an L3–L4 lumbar functional spine unit with poro-elastic constitutive equations. The aim of the study was to predict changes in the solid and fluid parameters of the IVD and CEP under structural changes in CEP. A compressive load of 500 N was applied followed by a 10 Nm moment in extension, flexion, lateral bending, and axial rotation to the L3–L4 model with fully saturated IVD, CEP, and cancellous bone. A healthy case of L3–L4 physiology was then compared to two cases of CEP sclerosis: a calcified cartilage endplate and a fluid constricted sclerotic cartilage endplate. Predicted NP fluid velocity increased for the calcified CEP and decreased for the calcified + less permeable CEP. Decreased NP fluid velocity was prominent in the axial direction through the CEP due to a less permeable path available for fluid flux. Fluid pressure and maximum principal stress in the NP were predicted to increase in both cases of CEP sclerosis compared to the healthy case. The porous medium predictions of this analysis agree with the hypothesis that CEP sclerosis decreases fluid flow out of the NP, builds up fluid pressure in the NP, and increases the stress concentrations in the NP solid matrix.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Adams M, McNally D, Dolan P (1996) ‘Stress’ distribution inside intervertebral discs. J Bone Joint Surg Br 78:965–972

    Article  Google Scholar 

  • Ayotte DC, Ito K, Perren SM, Tepic S (2000) Direction-dependent constriction flow in a poroelastic solid: the intervertebral disc valve. J Biomech Eng 122:587–593. https://doi.org/10.1115/1.1319658

    Article  Google Scholar 

  • Bian Q et al (2016) Excessive activation of TGFβ by spinal instability causes vertebral endplate sclerosis. Scientific reports 6:27093–27093. https://doi.org/10.1038/srep27093

    Article  Google Scholar 

  • Brinckmann P, Grootenboer H (1991) Change of disc height, radial disc bulge, and intradiscal pressure from discectomy an in vitro investigation on human lumbar discs. Spine 16:641–646

    Article  Google Scholar 

  • Dreischarf M et al (2014) Comparison of eight published static finite element models of the intact lumbar spine: predictive power of models improves when combined together. J Biomech 47:1757–1766

    Article  Google Scholar 

  • Erbulut DU, Zafarparandeh I, Hassan CR, Lazoglu I, Ozer AF (2015) Determination of the biomechanical effect of an interspinous process device on implanted and adjacent lumbar spinal segments using a hybrid testing protocol: a finite-element study. J Neurosurg Spine 23:200–208. https://doi.org/10.3171/2014.12.spine14419

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Fields AJ, Ballatori A, Liebenberg EC, Lotz JC (2018) Contribution of the endplates to disc degeneration. Current Molecular Biol Reports 4:151–160

    Article  Google Scholar 

  • Galbusera F, Schmidt H, Neidlinger-Wilke C, Gottschalk A, Wilke H-J (2011) The mechanical response of the lumbar spine to different combinations of disc degenerative changes investigated using randomized poroelastic finite element models. Euro Spine J 20:563–571. https://doi.org/10.1007/s00586-010-1586-4

    Article  Google Scholar 

  • Grunert P, Moriguchi Y, Grossbard BP, Ricart Arbona RJ, Bonassar LJ, Härtl R (2017) Degenerative changes of the canine cervical spine after discectomy procedures, an in vivo study. BMC Vet Res 13:193–193. https://doi.org/10.1186/s12917-017-1105-5

    Article  Google Scholar 

  • Guo L-X, Li R, Zhang M (2016) Biomechanical and fluid flowing characteristics of intervertebral disc of lumbar spine predicted by poroelastic finite element method. Acta Bioeng Biomech 18:19–29

    Google Scholar 

  • Hassan CR, Stinson M, von Nest N, Qin YX Stress and pore fluid alteration in degenerated lumbar intervertebral disk: a porous medium finite element study. In: 43rd Northeast Bioengineering Conference, Newark, NJ, 2017.

  • Heuer F, Schmitt H, Schmidt H, Claes L, Wilke H-J (2007) Creep associated changes in intervertebral disc bulging obtained with a laser scanning device. Clin Biomech 22:737–744

    Article  Google Scholar 

  • Horner HA, Urban JP (2001) 2001 Volvo Award Winner in basic science studies: effect of nutrient supply on the viability of cells from the nucleus pulposus of the intervertebral disc. Spine 26:2543–2549. https://doi.org/10.1097/00007632-200112010-00006

    Article  Google Scholar 

  • Jackson AR, Huang C-Y, Gu WY (2011) Effect of endplate calcification and mechanical deformation on the distribution of glucose in intervertebral disc: a 3D finite element study. Comp Methods Biomech Biomed Eng 14:195–204. https://doi.org/10.1080/10255842.2010.535815

    Article  Google Scholar 

  • Kiapour A, Ambati D, Hoy RW, Goel VK (2012) Effect of graded facetectomy on biomechanics of Dynesys dynamic stabilization system. Spine 37:E581–E589

    Article  Google Scholar 

  • Li H, Yan J-Z, Chen Y-J, Kang W-B, Huang J-X (2017) Non-invasive quantification of age-related changes in the vertebral endplate in rats using in vivo DCE-MRI. J Orthop Surg Res 12:169–169. https://doi.org/10.1186/s13018-017-0669-x

    Article  Google Scholar 

  • Lotz JC, Chin JR (2000) Intervertebral disc cell death is dependent on the magnitude and duration of spinal loading. Spine 25:1477–1483

    Article  Google Scholar 

  • Malandrino A, Planell JA, Lacroix D (2009) Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression, flexion and axial rotation. J Biomech 42:2780–2788

    Article  Google Scholar 

  • Panjabi MM (2007) Hybrid multidirectional test method to evaluate spinal adjacent-level effects.Clin Biomech 22:257–265. https://doi.org/10.1016/j.clinbiomech.2006.08.006

    Article  Google Scholar 

  • Roberts S, Urban JP, Evans H, Eisenstein SM (1996) Transport properties of the human cartilage endplate in relation to its composition and calcification. Spine 21:415–420

    Article  Google Scholar 

  • Rodriguez AG, Slichter CK, Acosta FL, Rodriguez-Soto AE, Burghardt AJ, Majumdar S, Lotz JC (2011) Human disc nucleus properties and vertebral endplate permeability.Spine 36:512–520 https://doi.org/10.1097/BRS.0b013e3181f72b94

    Article  Google Scholar 

  • Ruiz Wills C, Foata B, Gonzalez Ballester MA, Karppinen J, Noailly J (2018) Theoretical explorations generate new hypotheses about the role of the cartilage endplate in early intervertebral disk degeneration. Front Physiol 9:1210. https://doi.org/10.3389/fphys.2018.01210

    Article  Google Scholar 

  • Urban JP, Smith S, Fairbank JC (2004) Nutrition of the intervertebral disc. Spine 29:2700–2709. https://doi.org/10.1097/01.brs.0000146499.97948.52

    Article  Google Scholar 

  • Urban JPG, Roberts S (2003) Degeneration of the intervertebral disc. Arthritis Res Ther 5:120. https://doi.org/10.1186/ar629

    Article  Google Scholar 

  • Velísková P, Bashkuev M, Shirazi-Adl A, Schmidt H (2018) Computational study of the role of fluid content and flow on the lumbar disc response in cyclic compression: replication of in vitro and in vivo conditions. J Biomech 70:16–25. https://doi.org/10.1016/j.jbiomech.2017.10.032

    Article  Google Scholar 

  • Vos T et al (2012) Years lived with disability (YLDs) for 1160 sequelae of 289 diseases and injuries 1990–2010: a systematic analysis for the Global Burden of Disease Study 2010. Lancet 380:2163–2196. https://doi.org/10.1016/S0140-6736(12)61729-2

    Article  Google Scholar 

  • Wang Y, Videman T, Battié MC (2012) Lumbar vertebral endplate lesions: prevalence, classification, and association with age. Spine 37:1432–1439

    Article  Google Scholar 

  • Xu L, Chu B, Feng Y, Xu F, Zou Y-F (2016) Modic changes in lumbar spine: prevalence and distribution patterns of end plate oedema and end plate sclerosis. Br J Radiol 89:20150650

    Article  Google Scholar 

  • Yamamoto I, Panjabi MM, Crisco T, Oxland T (1989) Three-dimensional movements of the whole lumbar spine and lumbosacral joint. Spine 14:1256–1260. https://doi.org/10.1097/00007632-198911000-00020

    Article  Google Scholar 

  • Yuan W et al (2015) Establishment of intervertebral disc degeneration model induced by ischemic sub-endplate in rat tail. Spine J 15:1050–1059. https://doi.org/10.1016/j.spinee.2015.01.026

    Article  Google Scholar 

Download references

Acknowledgements

This work was kindly supported by the National Institute of Health (NIH) (R01AR52379 and R01AR61821). The authors wish to thank Nicholas van Nest and Michael Stinson for their excellent technical support with the finite element analysis.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yi-Xian Qin.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 25 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hassan, C.R., Lee, W., Komatsu, D.E. et al. Evaluation of nucleus pulposus fluid velocity and pressure alteration induced by cartilage endplate sclerosis using a poro-elastic finite element analysis. Biomech Model Mechanobiol 20, 281–291 (2021). https://doi.org/10.1007/s10237-020-01383-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-020-01383-8

Keywords

Navigation