A computational dynamic finite element simulation of the thoracic vertebrae under blunt loading: spinal cord injury

  • Hasan BiglariEmail author
  • Reza Razaghi
  • Sina Ebrahimi
  • Alireza Karimi
Technical Paper


Spinal cord is a long, thin, tubular bundle of nervous tissue located in the vertebral column. Since the spinal cord is one of the most crucial pathways for information connecting of the central nervous system, it has to stay safe under any blunt impact loading, i.e., accident, punch, gunshot, burst, etc. Therefore, it is important to investigate the possible injuries that may occur in the vertebral column, especially the spinal cord, as a result of blunt loading. However, due to various experimental limitations, numerical modelling, specifically finite element (FE) models, has been beneficial in predicting the injury to the spinal cord. This study, thus, aimed at predicting the stresses and deformations of a patient-specific FE model of the thoracic vertebral body, intervertebral disc, and spinal cord, which have been modelled according to the computed tomography/magnetic resonance imaging data, under blunt impact at different angles of 0°, 30°, and 45°. The model exhibited angle sensitive impact characteristics, and the stresses of the intervertebral disc and spinal cord significantly influenced the overall impact response in the simulated impact conditions. The highest amount of von Mises stresses in the vertebral body, intervertebral disc, and spinal cord was observed under the impact angle of 0° with 58.47, 7.26, and 0.13 MPa, respectively. The highest deformation in the spinal cord was 1.42 mm under the impact angle of 0°. The results of the this study have implications not only for understanding the stresses and deformations in the vertebral body, intervertebral disc, and spinal cord under the blunt loading, but also for providing a comprehensive information for the medical and biomechanical experts in regard to the role of the impact angle on the injury to the vertebral column.


Vertebral body Intervertebral disc Spinal cord Blunt loading Finite element modelling Injury 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Panjabi MM (1992) The stabilizing system of the spine. Part I. Function, dysfunction, adaptation, and enhancement. Clin Spine Surg 5:383–389Google Scholar
  2. 2.
    Bogduk N (2005) Clinical anatomy of the lumbar spine and sacrum. Elsevier, AmsterdamGoogle Scholar
  3. 3.
    Saifi C, Laratta JL, Petridis P, Shillingford JN, Lehman RA, Lenke LG (2017) Vertebral column resection for rigid spinal deformity. Global Spine J 7:280–290CrossRefGoogle Scholar
  4. 4.
    Gadow HF (2014) The evolution of the vertebral column. Cambridge University Press, CambridgeGoogle Scholar
  5. 5.
    Shapiro IM, Risbud MV (2014) Introduction to the structure, function, and comparative anatomy of the vertebrae and the intervertebral disc. The intervertebral disc. Springer, Berlin, pp 3–15Google Scholar
  6. 6.
    Nieuwenhuys R, Hans J, Nicholson C (2014) The central nervous system of vertebrates. Springer, BerlinGoogle Scholar
  7. 7.
    Yamasaki R, Lu H, Butovsky O, Ohno N, Rietsch AM, Cialic R et al (2014) Differential roles of microglia and monocytes in the inflamed central nervous system. J Exp Med 211:1533CrossRefGoogle Scholar
  8. 8.
    Mimata Y, Murakami H, Sato K, Suzuki Y (2014) Bilateral cerebellar and brain stem infarction resulting from vertebral artery injury following cervical trauma without radiographic damage of the spinal column: a case report. Skeletal Radiol 43:99–105CrossRefGoogle Scholar
  9. 9.
    Rao RD, Berry CA, Yoganandan N, Agarwal A (2014) Occupant and crash characteristics in thoracic and lumbar spine injuries resulting from motor vehicle collisions. Spine J 14:2355–2365CrossRefGoogle Scholar
  10. 10.
    Giordano C, Zappalà S, Kleiven S (2017) Anisotropic finite element models for brain injury prediction: the sensitivity of axonal strain to white matter tract inter-subject variability. Biomech Model Mechanobiol 16:1–25CrossRefGoogle Scholar
  11. 11.
    Drake AM, Takhounts EG, Hasija V (2017) Investigation of parameters affecting brain model validation and brain strains using the SIMon finite element head model. In: IRCOBI conference proceedingsGoogle Scholar
  12. 12.
    Bain AC, Meaney DF (2000) Tissue-level thresholds for axonal damage in an experimental model of central nervous system white matter injury. J Biomech Eng 122:615–622CrossRefGoogle Scholar
  13. 13.
    Galbraith J, Thibault L, Matteson D (1993) Mechanical and electrical responses of the squid giant axon to simple elongation. J Biomech Eng 115:13–22CrossRefGoogle Scholar
  14. 14.
    Wilcox RK, Allen DJ, Hall RM, Limb D, Barton DC, Dickson RA (2004) A dynamic investigation of the burst fracture process using a combined experimental and finite element approach. Eur Spine J 13:481–488CrossRefGoogle Scholar
  15. 15.
    Wilcox RK, Boerger TO, Allen DJ, Barton DC, Limb D, Dickson RA et al (2003) A dynamic study of thoracolumbar burst fractures. JBJS 85:2184–2189CrossRefGoogle Scholar
  16. 16.
    ‘Dale’ Bass CR, Rafaels KA, Salzar RS, Carboni M, Kent RW, Lloyd MD et al (2008) Thoracic and lumbar spinal impact tolerance. Accid Anal Prev 40:487–495CrossRefGoogle Scholar
  17. 17.
    Du C, Mo Z, Tian S, Wang L, Fan J, Liu S et al (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 30:1121–1131CrossRefGoogle Scholar
  18. 18.
    Ruan J, El-Jawahri R, Li C, Barbat S, Prasad P (2003) Prediction and analysis of human thoracic impact responses and injuries in cadaver impacts using a full human body finite element model. Stapp Car Crash J 47:299Google Scholar
  19. 19.
    Karimi A, Shojaei A, Tehrani P (2017) Mechanical properties of the human spinal cord under the compressive loading. J Chem Neuroanat 86:15–18CrossRefGoogle Scholar
  20. 20.
    Karimi A, Razaghi R, Navidbakhsh M, Sera T, Kudo S (2016) Quantifying the injury of the human eye components due to tennis ball impact using a computational fluid–structure interaction model. Sports Eng 19:105–115CrossRefGoogle Scholar
  21. 21.
    Mimics Student Edition Course Book, MIMICS, Belgium.
  22. 22.
    Hallquist JO (2006) LS-DYNA theory manual. Livermore software Technology corporation. 3:25–31Google Scholar
  23. 23.
    Yoganandan N, Kumaresan S, Voo L, Pintar FA (1996) Finite element applications in human cervical spine modeling. Spine 21:1824–1834CrossRefGoogle Scholar
  24. 24.
    Dreischarf M, Zander T, Shirazi-Adl A, Puttlitz CM, Adam CJ, Chen CS et al (2014) Comparison of eight published static finite element models of the intact lumbar spine: predictive power of models improves when combined together. 1766 47:1757Google Scholar
  25. 25.
    Karimi A, Navidbakhsh M, Razaghi R (2014) An experimental-finite element analysis on the kinetic energy absorption capacity of polyvinyl alcohol sponge. Mater Sci Eng, C 39:253–258CrossRefGoogle Scholar
  26. 26.
    Tran NT, Watson NA, Tencer AF, Ching RP, Anderson PA (1995) Mechanism of the burst fracture in the thoracolumbar spine. The effect of loading rate. Spine 20:1984–1988CrossRefGoogle Scholar
  27. 27.
    Panjabi MM, Oxland TR, Lin R-M, McGowen TW (1994) Thoracolumbar burst fracture. A biomechanical investigation of its multidirectional flexibility. Spine 19:578–585CrossRefGoogle Scholar
  28. 28.
    Lin RM, Panjabi MM, Oxland TR (1993) Functional radiographs of acute thoracolumbar burst fractures. A biomechanical study. Spine 18:2431–2437CrossRefGoogle Scholar
  29. 29.
    Zou D, Yoo JU, Edwards WT, Donovan DM, Chang KW, Bayley JC et al (1993) Mechanics of anatomic reduction of thoracolumbar burst fractures. Comparison of distraction versus distraction plus lordosis, in the anatomic reduction of the thoracolumbar burst fracture. Spine 18:195–203CrossRefGoogle Scholar
  30. 30.
    Shirazi-Adl A, Ahmed AM, Shrivastava SC (1986) Mechanical response of a lumbar motion segment in axial torque alone and combined with compression. Spine 11:914–927CrossRefGoogle Scholar
  31. 31.
    Hongo M, Abe E, Shimada Y, Murai H, Ishikawa N, Sato K (1999) Surface strain distribution on thoracic and lumbar vertebrae under axial compression: the role in burst fractures. Spine 24:1197–1202CrossRefGoogle Scholar
  32. 32.
    El-Rich M, Arnoux P-J, Wagnac E, Brunet C, Aubin C-E (2009) Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions. J Biomech 42:1252–1262CrossRefGoogle Scholar
  33. 33.
    Greaves CY, Gadala MS, Oxland TR (2008) A three-dimensional finite element model of the cervical spine with spinal cord: an investigation of three injury mechanisms. Ann Biomed Eng 36:396CrossRefGoogle Scholar
  34. 34.
    Marini G, Studer H, Huber G, Püschel K, Ferguson SJ (2016) Geometrical aspects of patient-specific modelling of the intervertebral disc: collagen fibre orientation and residual stress distribution. Biomech Model Mechanobiol 15:543–560CrossRefGoogle Scholar
  35. 35.
    Koser DE, Moeendarbary E, Hanne J, Kuerten S, Franze K (2015) CNS cell distribution and axon orientation determine local spinal cord mechanical properties. Biophys J 108:2137–2147CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Hasan Biglari
    • 1
    Email author
  • Reza Razaghi
    • 1
    • 4
  • Sina Ebrahimi
    • 2
  • Alireza Karimi
    • 3
  1. 1.Department of Mechanical EngineeringUniversity of TabrizTabrizIran
  2. 2.Department of Mechanical EngineeringSharif University of TechnologyTehranIran
  3. 3.Department of Mechanical EngineeringKyushu UniversityFukuokaJapan
  4. 4.Basir Eye Health Research CenterTehranIran

Personalised recommendations