Skip to main content

Advertisement

SpringerLink
Log in

A probabilistic finite element analysis of the stresses in the augmented vertebral body after vertebroplasty

  • Original Article
  • Published:
European Spine Journal Aims and scope Submit manuscript

Abstract

Fractured vertebral bodies are often stabilized by vertebroplasty. Several parameters, including fracture type, cement filling shape, cement volume, elastic moduli of cement, cancellous bone and fractured region, may all affect the stresses in the augmented vertebral body and in bone cement. The aim of this study was to determine numerically the effects of these input parameters on the stresses caused. In a probabilistic finite element study, an osteoligamentous model of the lumbar spine was employed. Seven input parameters were simultaneously and randomly varied within appropriate limits for >110 combinations thereof. The maximum von Mises stresses in cancellous and cortical bone of the treated vertebral body L3 and in bone cement were calculated. The loading cases standing, flexion, extension, lateral bending, axial rotation and walking were simulated. In a subsequent sensitivity analysis, the coefficients of correlation and determination of the input parameters on the von Mises stresses were calculated. The loading case has a strong influence on the maximum von Mises stress. In cancellous bone, the median value of the maximum von Mises stresses for the different input parameter combinations varied between 1.5 (standing) and 4.5 MPa (flexion). The ranges of the stresses are large for all loading cases studied. Depending on the loading case, up to 69% of the maximum stress variation could be explained by the seven input parameters. The fracture shape and the elastic modulus of the fractured region have the highest influence. In cortical bone, the median values of the maximum von Mises stresses varied between 31.1 (standing) and 61.8 MPa (flexion). The seven input parameters could explain up to 80% of the stress variation here. It is the fracture shape, which has always the highest influence on the stress variation. In bone cement, the median value of the maximum von Mises stresses varied between 3.8 (standing) and 12.7 MPa (flexion). Up to 75% of the maximum stress variation in cement could be explained by the seven input parameters. Fracture shape, and the elastic moduli of bone cement and of the fracture region are those input parameters with the highest influence on the stress variation. In the model with no fracture, the maximum von Mises stresses are generally low. The present probabilistic and sensitivity study clearly showed that in vertebroplasty the maximum stresses in the augmented vertebral body and in bone cement depend mainly on the loading case and fracture shape. Elastic moduli of cement, fracture region and cancellous bone as well as cement volume have sometimes a moderate effect while number and symmetry of cement plugs have virtually no effect on the maximum stresses.

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

Access this article

Log in via an institution

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
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Heini PF, Orler R (2004) Kyphoplasty for treatment of osteoporotic vertebral fractures. Eur Spine J 13:184–192

    Article  PubMed  Google Scholar 

  2. Garfin SR, Yuan HA, Reiley MA (2001) New technologies in spine: kyphoplasty and vertebroplasty for the treatment of painful osteoporotic compression fractures. Spine 26:1511–1515

    Article  CAS  PubMed  Google Scholar 

  3. Blattert TR, Jestaedt L, Weckbach A (2009) Suitability of a calcium phosphate cement in osteoporotic vertebral body fracture augmentation: a controlled, randomized, clinical trial of balloon kyphoplasty comparing calcium phosphate versus polymethylmethacrylate. Spine (Phila Pa 1976) 34:108–114

    Google Scholar 

  4. Magerl F, Aebi M, Gertzbein SD, Harms J, Nazarian S (1994) A comprehensive classification of thoracic and lumbar injuries. Eur Spine J 3:184–201

    Article  CAS  PubMed  Google Scholar 

  5. Shin DA, Kim KN, Shin HC, Kim SH, Yoon DH (2008) Progressive collapse of PMMA-augmented vertebra: a report of three cases. Zentralbl Neurochir 69:43–46

    Article  CAS  PubMed  Google Scholar 

  6. Belkoff SM, Mathis JM, Jasper LE, Deramond H (2001) The biomechanics of vertebroplasty. The effect of cement volume on mechanical behavior. Spine 26:1537–1541

    Article  CAS  PubMed  Google Scholar 

  7. Liebschner MA, Rosenberg WS, Keaveny TM (2001) Effects of bone cement volume and distribution on vertebral stiffness after vertebroplasty. Spine 26:1547–1554

    Article  CAS  PubMed  Google Scholar 

  8. Molloy S, Mathis JM, Belkoff SM (2003) The effect of vertebral body percentage fill on mechanical behavior during percutaneous vertebroplasty. Spine 28:1549–1554

    Article  PubMed  Google Scholar 

  9. Rohlmann A, Zander T, Jony A, Weber U, Bergmann G (2005) Einfluss der Wirbelkörpersteifigkeit vor und nach Vertebroplastik auf den intradiskalen Druck. Biomed Tech (Berl) 50:148–152

    Article  CAS  Google Scholar 

  10. Sun K, Liebschner MA (2004) Biomechanics of prophylactic vertebral reinforcement. Spine 29:1428–1435

    Article  PubMed  Google Scholar 

  11. Baroud G, Nemes J, Heini P, Steffen T (2003) Load shift of the intervertebral disc after a vertebroplasty: a finite-element study. Eur Spine J 12:421–426

    Article  CAS  PubMed  Google Scholar 

  12. Polikeit A, Nolte LP, Ferguson SJ (2003) The effect of cement augmentation on the load transfer in an osteoporotic functional spinal unit: finite-element analysis. Spine 28:991–996

    Article  PubMed  Google Scholar 

  13. Rohlmann A, Zander T, Bergmann G (2006) Spinal loads after osteoporotic vertebral fractures treated by vertebroplasty or kyphoplasty. Eur Spine J 15:1255–1264

    Article  PubMed  Google Scholar 

  14. Villarraga LM, Cripton PA, Bellezza AJ, Berlemann U, Kurtz SM, Edidin AA (2004) Knochen und Knochen-Zement-Belastungen in der thorakolumbalen Wirbelsäule nach Kyphoplastik. Eine Finite-Element-Studie. Orthopade 33:48–55

    Article  Google Scholar 

  15. Chevalier Y, Pahr D, Charlebois M, Heini P, Schneider E, Zysset P (2008) Cement distribution, volume, and compliance in vertebroplasty: some answers from an anatomy-based nonlinear finite element study. Spine 33:1722–1730

    Article  PubMed  Google Scholar 

  16. Teo J, Wang SC, Teoh SH (2007) Preliminary study on biomechanics of vertebroplasty: a computational fluid dynamics and solid mechanics combined approach. Spine 32:1320–1328

    Article  PubMed  Google Scholar 

  17. Keller TS, Kosmopoulos V, Lieberman IH (2005) Vertebroplasty and kyphoplasty affect vertebral motion segment stiffness and stress distributions: a microstructural finite-element study. Spine 30:1258–1265

    Article  PubMed  Google Scholar 

  18. Haldar A, Mahadevan S (2000) Probability, reliability, and statistical methods in engineering design. Wiley, New York

    Google Scholar 

  19. Dar FH, Meakin JR, Aspden RM (2002) Statistical methods in finite element analysis. J Biomech 35:1155–1161

    Article  PubMed  Google Scholar 

  20. Ananthakrishnan D, Berven S, Deviren V, Cheng K, Lotz JC, Xu Z, Puttlitz CM (2005) The effect on anterior column loading due to different vertebral augmentation techniques. Clin Biomech (Bristol, Avon) 20:25–31

    Article  Google Scholar 

  21. Davis JW, Grove JS, Wasnich RD, Ross PD (1999) Spatial relationships between prevalent and incident spine fractures. Bone 24:261–264

    Article  CAS  PubMed  Google Scholar 

  22. Jensen ME, Dion JE (2000) Percutaneous vertebroplasty in the treatment of osteoporotic compression fractures. Neuroimaging Clin N Am 10:547–568

    CAS  PubMed  Google Scholar 

  23. Wilcox RK (2006) The biomechanical effect of vertebroplasty on the adjacent vertebral body: a finite element study. Proc Inst Mech Eng [H] 220:565–572

    CAS  Google Scholar 

  24. Zander T, Rohlmann A, Bock B, Bergmann G (2007) Biomechanische Konsequenzen von verschiedenen Positionierungen bewegungserhaltender Bandscheibenimplantate. Eine Finite-Elemente-Studie an der Lendenwirbelsäule. Orthopade 36:205–211

    Article  CAS  PubMed  Google Scholar 

  25. Zander T, Rohlmann A, Calisse J, Bergmann G (2001) Estimation of muscle forces in the lumbar spine during upper-body inclination. Clin Biomech 16:S73–S80

    Article  Google Scholar 

  26. Rohlmann A, Bauer L, Zander T, Bergmann G, Wilke HJ (2006) Determination of trunk muscle forces for flexion and extension by using a validated finite element model of the lumbar spine and measured in vivo data. J Biomech 39:981–989

    Article  PubMed  Google Scholar 

  27. Zander T, Rohlmann A, Bergmann G (2009) Influence of different artificial disc kinematics on spine biomechanics. Clin Biomech (Bristol, Avon) 24:135–142

    Article  Google Scholar 

  28. Rohlmann A, Zander T, Bock B, Bergmann G (2008) Effect of position and height of a mobile core type artificial disc on the biomechanical behaviour of the lumbar spine. Proc Inst Mech Eng [H] 222:229–239

    CAS  Google Scholar 

  29. Eberlein R, Holzapfel GA, Schulze-Bauer CAJ (2000) An anisotropic model for annulus tissue and enhanced finite element analysis of intact lumbar disc bodies. Comp Meth Biomech Biomed Eng 4:209–229

    Article  Google Scholar 

  30. Rohlmann A, Zander T, Bergmann G (2005) Effect of total disc replacement with ProDisc on the biomechanical behavior of the lumbar spine. Spine 30:738–743

    Article  PubMed  Google Scholar 

  31. Nolte LP, Panjabi MM, Oxland TR (1990) Biomechanical properties of lumbar spinal ligaments. In: Heimke G, Soltesz U, Lee AJC (eds) Clinical implant materials, advances in biomaterials, vol 9. Elsevier, Heidelberg, pp 663–668

    Google Scholar 

  32. 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  CAS  PubMed  Google Scholar 

  33. Ueno K, Liu YK (1987) A three-dimensional nonlinear finite element model of lumbar intervertebral joint in torsion. J Biomech Eng 109:200–209

    Article  CAS  PubMed  Google Scholar 

  34. Patwardhan AG, Havey RM, Meade KP, Lee B, Dunlap B (1999) A follower load increases the load-carrying capacity of the lumbar spine in compression. Spine 24:1003–1009

    Article  CAS  PubMed  Google Scholar 

  35. Rohlmann A, Neller S, Claes L, Bergmann G, Wilke H-J (2001) Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine. Spine 26:E557–E561

    Article  CAS  PubMed  Google Scholar 

  36. Rohlmann A, Zander T, Rao M, Bergmann G (2009) Applying a follower load delivers realistic results for simulating standing. J Biomech 42:1520–1526

    Article  CAS  PubMed  Google Scholar 

  37. Rohlmann A, Zander T, Rao M, Bergmann G (2009) Realistic loading conditions for upper body bending. J Biomech 42:884–890

    Article  CAS  PubMed  Google Scholar 

  38. Rohlmann A, Claes L, Bergmann G, Graichen F, Neef P, Wilke H-J (2001) Comparison of intradiscal pressures and spinal fixator loads for different body positions and exercises. Ergonomics 44:781–794

    Article  Google Scholar 

  39. Rozumalski A, Schwartz MH, Wervey R, Swanson A, Dykes DC, Novacheck T (2008) The in vivo three-dimensional motion of the human lumbar spine during gait. Gait Posture 28:378–384

    Article  PubMed  Google Scholar 

  40. Gurdak JJ, McCray JE, Thyne G, Qi SL (2007) Latin hypercube approach to estimate uncertainty in ground water vulnerability. Ground Water 45:348–361

    Article  CAS  PubMed  Google Scholar 

  41. Hulme PA, Boyd SK, Heini PF, Ferguson SJ (2009) Differences in endplate deformation of the adjacent and augmented vertebra following cement augmentation. Eur Spine J 18:614–623

    Article  PubMed  Google Scholar 

  42. Fyhrie DP, Vashishth D (2000) Bone stiffness predicts strength similarly for human vertebral cancellous bone in compression and for cortical bone in tension. Bone 26:169–173

    Article  CAS  PubMed  Google Scholar 

  43. Ikenaga M, Hardouin P, Lemaitre J, Andrianjatovo H, Flautre B (1998) Biomechanical characterization of a biodegradable calcium phosphate hydraulic cement: a comparison with porous biphasic calcium phosphate ceramics. J Biomed Mater Res 40:139–144

    Article  CAS  PubMed  Google Scholar 

  44. Goel VK, Ramirez SA, Kong W, Gilbertson LG (1995) Cancellous bone Young’s modulus variation within the vertebral body of a ligamentous lumbar spine—application of bone adaptive remodeling concepts. J Biomech Eng 117:266–271

    Article  CAS  PubMed  Google Scholar 

  45. Shirazi-Adl SA, Shrivastava SC, Ahmed AM (1984) Stress analysis of the lumbar disc-body unit in compression. A three-dimensional nonlinear finite element study. Spine 9:120–134

    Article  CAS  PubMed  Google Scholar 

  46. Rohlmann A, Zander T, Schmidt H, Wilke H-J, Bergmann G (2006) Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method. J Biomech 39:2484–2490

    Article  PubMed  Google Scholar 

  47. Sharma M, Langrana NA, Rodriguez J (1995) Role of ligaments and facets in lumbar spinal stability. Spine 20:887–900

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

This study was financially supported by Heraeus Medical GmbH, Wehrheim, Germany and the Deutsche Forschungsgemeinschaft, Bonn, Germany (Ro 581/17-2). Finite element analyses were performed at the Norddeutscher Verbund für Hoch-und Höchstleistungsrechnen (HLRN). The authors thank N.K. Burra for technical assistance.

Author information

Authors and Affiliations

  1. Julius Wolff Institut, Charité-Universitätsmedizin Berlin, Augustenburger Platz 1, 13353, Berlin, Germany

    Antonius Rohlmann, Hadi Nabil Boustani, Georg Bergmann & Thomas Zander

Authors
  1. Antonius Rohlmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hadi Nabil Boustani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Georg Bergmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thomas Zander
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonius Rohlmann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rohlmann, A., Boustani, H.N., Bergmann, G. et al. A probabilistic finite element analysis of the stresses in the augmented vertebral body after vertebroplasty. Eur Spine J 19, 1585–1595 (2010). https://doi.org/10.1007/s00586-010-1386-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00586-010-1386-x

Keywords

Search

Navigation