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Stiffness and Strength Predictions From Finite Element Models of the Knee are Associated with Lower-Limb Fractures After Spinal Cord Injury

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Abstract

Spinal cord injury (SCI) is associated with bone fragility and fractures around the knee. The purpose of this investigation was to validate a computed tomography (CT) based finite element (FE) model of the proximal tibia and distal femur under biaxial loading, and to retrospectively quantify the relationship between model predictions and fracture incidence. Twenty-six cadaveric tibiae and femora (n = 13 each) were loaded to 300 N of compression, then internally rotated until failure. FE predictions of torsional stiffness (K) and strength (Tult) explained 74% (n = 26) and 93% (n = 7) of the variation in experimental measurements, respectively. Univariate analysis and logistic regression were subsequently used to determine if FE predictions and radiographic measurements from CT and dual energy X-ray absorptiometry (DXA) were associated with prevalent lower-limb fracture in 50 individuals with SCI (n = 14 fractures). FE and CT measures, but not DXA, were lower in individuals with fracture. FE predictions of Tult at the tibia demonstrated the highest odds ratio (4.98; p = 0.006) and receiver operating characteristic (0.84; p = 0.008) but did not significantly outperform other metrics. In conclusion, CT-based FE model predictions were associated with prevalent fracture risk after SCI; this technique could be a powerful tool in future clinical research.

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References

  1. Abderhalden, L., F. M. Weaver, M. Bethel, H. Demirtas, S. Burns, J. Svircev, H. Hoenig, K. Lyles, S. Miskevics, and L. D. Carbone. Dual-energy X-ray absorptiometry and fracture prediction in patients with spinal cord injuries and disorders. Osteoporos. Int. 28:925–934, 2017.

    CAS  PubMed  Google Scholar 

  2. Biering-Serensen, F., H. Bohr, and O. Schaadt. Bone mineral content of the lumbar spine and lower extremities years after spinal cord lesion. Paraplegia 26:293–301, 1988.

    Google Scholar 

  3. Biering-Sorensen, F., H. H. Bohr, and O. P. Schaadt. Longitudinal study of bone mineral content in the lumbar spine, the forearm and the lower extremities after spinal cord injury. Eur. J. Clin. Invest. 20:330–335, 1990.

    CAS  PubMed  Google Scholar 

  4. Cezayirlioglu, H., E. Bahniuk, D. T. Davy, and K. G. Heiple. Anisotropic yield behavior of bone under combined axial force and torque. J. Biomech. 18:61–69, 1985.

    CAS  PubMed  Google Scholar 

  5. Cirnigliaro, C. M., M. J. Myslinski, M. F. La Fountaine, S. C. Kirshblum, G. F. Forrest, and W. A. Bauman. Bone loss at the distal femur and proximal tibia in persons with spinal cord injury: imaging approaches, risk of fracture, and potential treatment options. Osteoporos. Int. 28:747–765, 2017.

    CAS  PubMed  Google Scholar 

  6. Cody, D. D., G. J. Gross, F. J. Hou, H. J. Spencer, S. A. Goldstein, and D. P. Fyhrie. Femoral strength is better predicted by finite element models than QCT and DXA. J. Biomech. 32:1013–1020, 1999.

    CAS  PubMed  Google Scholar 

  7. Crawford, R. P., C. E. Cann, and T. M. Keaveny. Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography. Bone 33:744–750, 2003.

    PubMed  Google Scholar 

  8. Currey, J. D. Tensile yield in compact bone is determined by strain, post-yield behaviour by mineral content. J. Biomech. 37:549–556, 2004.

    PubMed  Google Scholar 

  9. Edwards, W. B., T. J. Schnitzer, and K. L. Troy. Bone mineral and stiffness loss at the distal femur and proximal tibia in acute spinal cord injury. Osteoporos. Int. 24:2461–2469, 2013.

    CAS  PubMed  Google Scholar 

  10. Edwards, W. B., T. J. Schnitzer, and K. L. Troy. Torsional stiffness and strength of the proximal tibia are better predicted by finite element models than DXA or QCT. J. Biomech. 46:1655–1662, 2013.

    PubMed  PubMed Central  Google Scholar 

  11. Edwards, W. B., T. J. Schnitzer, and K. L. Troy. The mechanical consequence of actual bone loss and simulated bone recovery in acute spinal cord injury. Bone 60:141–147, 2014.

    PubMed  Google Scholar 

  12. Edwards, W. B., N. Simonian, I. T. Haider, A. S. Anschel, D. Chen, K. E. Gordon, E. K. Gregory, K. H. Kim, R. Parachuri, K. L. Troy, and T. J. Schnitzer. Effects of teriparatide and vibration on bone mass and bone strength in people with bone loss and spinal cord injury: a randomized controlled trial. J. Bone Miner. Res. 33:1729–1740, 2018.

    CAS  PubMed  Google Scholar 

  13. Edwards, W. B., N. Simonian, K. L. Troy, and T. J. Schnitzer. Reduction in torsional stiffness and strength at the proximal tibia as a function of time since spinal cord injury. J. Bone Miner. Res. 30:1422–1430, 2015.

    CAS  PubMed  Google Scholar 

  14. Edwards, W. B., and K. L. Troy. Finite element prediction of surface strain and fracture strength at the distal radius. Med. Eng. Phys. 34:290–298, 2012.

    PubMed  Google Scholar 

  15. Eser, P., A. Frotzler, Y. Zehnder, and J. Denoth. Fracture threshold in the femur and tibia of people with spinal cord injury as determined by peripheral quantitative computed tomography. Arch. Phys. Med. Rehabil. 2005. https://doi.org/10.1016/j.apmr.2004.09.006.

    Article  PubMed  Google Scholar 

  16. Eser, P., A. Frotzler, Y. Zehnder, L. Wick, H. Knecht, J. Denoth, and H. Schiessl. Relationship between the duration of paralysis and bone structure: a pQCT study of spinal cord injured individuals. Bone 34:869–880, 2004.

    CAS  PubMed  Google Scholar 

  17. Frey-Rindova, P., E. D. De Bruin, E. Stüssi, M. A. Dambacher, and V. Dietz. Bone mineral density in upper and lower extremities during 12 months after spinal cord injury measured by peripheral quantitative computed tomography. Spinal Cord 38:26–32, 2000.

    CAS  PubMed  Google Scholar 

  18. Garland, D., R. Adkins, and C. Stewart. Fracture threshold and risk for osteoporosis and pathologic fractures in individuals with spinal cord injury. Top. Spinal Cord Inj. Rehabil. 11:61–69, 2005.

    Google Scholar 

  19. Gordon, K. E., M. J. Wald, and T. J. Schnitzer. Effect of parathyroid hormone combined with gait training on bone density and bone architecture in people with chronic spinal cord injury. PM&R 5:663–671, 2013.

    Google Scholar 

  20. Grassner, L., B. Klein, D. Maier, V. Bühren, and M. Vogel. Lower extremity fractures in patients with spinal cord injury characteristics, outcome and risk factors for non-unions. J. Spinal Cord Med. 41:676–683, 2018.

    PubMed  Google Scholar 

  21. Gray, H. A., F. Taddei, A. B. Zavatsky, L. Cristofolini, and H. S. Gill. Experimental validation of a finite element model of a human cadaveric tibia. J. Biomech. Eng. 130:031016, 2008.

    PubMed  Google Scholar 

  22. Haider, I. T., S. M. Lobos, N. Simonian, T. J. Schnitzer, and W. B. Edwards. Bone fragility after spinal cord injury: reductions in stiffness and bone mineral at the distal femur and proximal tibia as a function of time. Osteoporos. Int. 30:1422–1430, 2018.

    Google Scholar 

  23. Haider, I. T., N. Simonian, A. S. Saini, F. M. Leung, W. B. Edwards, and T. J. Schnitzer. Open-label clinical trial of alendronate after teriparatide therapy in people with spinal cord injury and low bone mineral density. Spinal Cord 57:832–842, 2019.

    PubMed  Google Scholar 

  24. Hayes, W. C., and D. R. Carter. Postyield behavior of subchondral trabecular bone. J. Biomed. Mater. Res. 10:537–544, 1976.

    CAS  PubMed  Google Scholar 

  25. Hill, R. A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. A Math. Phys. Eng. Sci. 193:281–297, 1948.

    CAS  Google Scholar 

  26. Imai, K., I. Ohnishi, T. Matsumoto, S. Yamamoto, and K. Nakamura. Assessment of vertebral fracture risk and therapeutic effects of alendronate in postmenopausal women using a quantitative computed tomography-based nonlinear finite element method. Osteoporos. Int. 20:801–810, 2009.

    CAS  PubMed  Google Scholar 

  27. Keating, J. F., M. Kerr, and M. Delargy. Minimal trauma causing fractures in patients with spinal cord injury. Disabil. Rehabil. 14:108–109, 1992.

    CAS  PubMed  Google Scholar 

  28. Kirshblum, S. C., W. Waring, F. Biering-Sorensen, S. P. Burns, M. Johansen, M. Schmidt-Read, W. Donovan, D. Graves, A. Jha, L. Jones, M. J. Mulcahey, and A. Krassioukov. International standards for neurological classification of spinal cord injury (Revised 2011). J. Spinal Cord Med. 34:547–554, 2011.

    PubMed  PubMed Central  Google Scholar 

  29. Lala, D., B. C. Craven, L. Thabane, A. Papaioannou, J. D. Adachi, M. R. Popovic, and L. M. Giangregorio. Exploring the determinants of fracture risk among individuals with spinal cord injury. Osteoporos. Int. 25:177–185, 2014.

    CAS  PubMed  Google Scholar 

  30. Lambach, R. L., N. E. Stafford, J. A. Kolesar, B. J. Kiratli, G. H. Creasey, R. S. Gibbons, B. J. Andrews, and G. S. Beaupre. Bone changes in the lower limbs from participation in an FES rowing exercise program implemented within two years after traumatic spinal cord injury. J. Spinal Cord Med. 43:306–314, 2018.

    PubMed  PubMed Central  Google Scholar 

  31. Lazo, M. G., P. Shirazi, M. Sam, A. Giobbie-Hurder, M. J. Blacconiere, and M. Muppidi. Osteoporosis and risk of fracture in men with spinal cord injury. Spinal Cord 39:208–214, 2001.

    CAS  PubMed  Google Scholar 

  32. Les, C. M., S. M. Stover, J. H. Keyak, K. T. Taylor, and A. J. Kaneps. Stiff and strong compressive properties are associated with brittle post-yield behavior in equine compact bone material. J. Orthop. Res. 20:607–614, 2002.

    CAS  PubMed  Google Scholar 

  33. Lewis, G. Properties of acrylic bone cement: state of the art review. J. Biomed. Mater. Res. 38:155–182, 1997.

    CAS  PubMed  Google Scholar 

  34. Martínez, Á. A., J. Cuenca, A. Herrera, and J. Domingo. Late lower extremity fractures in patients with paraplegia. Injury 33:583–586, 2002.

    PubMed  Google Scholar 

  35. McPherson, J. G., W. B. Edwards, A. Prasad, K. L. Troy, J. W. Griffith, and T. J. Schnitzer. Dual energy X-ray absorptiometry of the knee in spinal cord injury: methodology and correlation with quantitative computed tomography. Spinal Cord 52:821–825, 2014.

    CAS  PubMed  Google Scholar 

  36. Modlesky, C. M., S. Majumdar, A. Narasimhan, and G. A. Dudley. Trabecular bone microarchitecture is deteriorated in men with spinal cord injury. J. Bone Miner. Res. 19:48–55, 2004.

    PubMed  Google Scholar 

  37. Moons, K. G. M., J. A. H. de Groot, W. Bouwmeester, Y. Vergouwe, S. Mallett, D. G. Altman, J. B. Reitsma, and G. S. Collins. Critical appraisal and data extraction for systematic reviews of prediction modelling studies: the CHARMS checklist. PLoS Med. 11:15, 2014. https://doi.org/10.1371/journal.pmed.1001744.

    Article  Google Scholar 

  38. Morgan, E. F., H. H. Bayraktar, and T. M. Keaveny. Trabecular bone modulus–density relationships depend on anatomic site. J. Biomech. 36:897–904, 2003.

    PubMed  Google Scholar 

  39. Morse, L. R., K. L. Troy, Y. Fang, N. Nguyen, R. Battaglino, R. F. Goldstein, R. Gupta, and J. A. Taylor. Combination therapy with zoledronic acid and FES-row training mitigates bone loss in paralyzed legs: results of a randomized comparative clinical trial. JBMR Plus 3:e10167, 2019.

    CAS  PubMed  PubMed Central  Google Scholar 

  40. Nishiyama, K. K., S. Gilchrist, P. Guy, P. Cripton, and S. K. Boyd. Proximal femur bone strength estimated by a computationally fast finite element analysis in a sideways fall configuration. J. Biomech. 46:1231–1236, 2013.

    PubMed  Google Scholar 

  41. Orwoll, E. S., L. M. Marshall, C. M. Nielson, S. R. Cummings, J. Lapidus, J. A. Cauley, K. Ensrud, N. Lane, P. R. Hoffmann, D. L. Kopperdahl, and T. M. Keaveny. Finite element analysis of the proximal femur and hip fracture risk in older men. J. Bone Miner. Res. 24:475, 2009.

    PubMed  Google Scholar 

  42. Reiter, A. L., A. Volk, J. Vollmar, B. Fromm, and H. J. Gerner. Changes of basic bone turnover parameters in short-term and long-term patients with spinal cord injury. Eur. Spine J. 16:771–776, 2007.

    PubMed  Google Scholar 

  43. Schileo, E., F. Taddei, L. Cristofolini, and M. Viceconti. Subject-specific finite element models implementing a maximum principal strain criterion are able to estimate failure risk and fracture location on human femurs tested in vitro. J. Biomech. 41:356–367, 2008.

    PubMed  Google Scholar 

  44. Vestergaard, P., K. Krogh, L. Rejnmark, and L. Mosekilde. Fracture rates and risk factors for fractures in patients with spinal cord injury. Spinal Cord 36:790–796, 1998.

    CAS  PubMed  Google Scholar 

  45. Zehnder, Y., M. Lüthi, D. Michel, H. Knecht, R. Perrelet, I. Neto, M. Kraenzlin, G. Zäch, and K. Lippuner. Long-term changes in bone metabolism, bone mineral density, quantitative ultrasound parameters, and fracture incidence after spinal cord injury: a cross-sectional observational study in 100 paraplegic men. Osteoporos. Int. 15:180–189, 2004.

    PubMed  Google Scholar 

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Acknowledgments

This study was funded by the Department of Defense U.S. Army Medical Research and Materiel Command (Grant #: SC090010 and BA150039). Research infrastructure for this study was funded by a Canadian Foundation for Innovation (CFI) John R. Evans Leaders Fund (JELF; Project #37134).

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Authors and Affiliations

  1. Human Performance Laboratory, Faculty of Kinesiology, University of Calgary, Calgary, Canada

    Ifaz T. Haider & W. Brent Edwards

  2. McCaig Institute for Bone and Joint Health, University of Calgary, Calgary, Canada

    Ifaz T. Haider & W. Brent Edwards

  3. Department of Physical Medicine and Rehabilitation, Northwestern University Feinberg School of Medicine, Chicago, USA

    Narina Simonian & Thomas J. Schnitzer

  4. Northwestern University Clinical and Translational Sciences Institute, Northwestern University Feinberg School of Medicine, Chicago, USA

    Narina Simonian

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  1. Ifaz T. Haider
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  2. Narina Simonian
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Correspondence to Ifaz T. Haider.

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Associate Editor Eiji Tanaka oversaw the review of this article.

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Haider, I.T., Simonian, N., Schnitzer, T.J. et al. Stiffness and Strength Predictions From Finite Element Models of the Knee are Associated with Lower-Limb Fractures After Spinal Cord Injury. Ann Biomed Eng 49, 769–779 (2021). https://doi.org/10.1007/s10439-020-02606-w

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