Annals of Biomedical Engineering

, Volume 43, Issue 10, pp 2503–2514 | Cite as

Development and Validation of Statistical Models of Femur Geometry for Use with Parametric Finite Element Models

  • Katelyn F. Klein
  • Jingwen Hu
  • Matthew P. Reed
  • Carrie N. Hoff
  • Jonathan D. Rupp


Statistical models were developed that predict male and female femur geometry as functions of age, body mass index (BMI), and femur length as part of an effort to develop lower-extremity finite element models with geometries that are parametric with subject characteristics. The process for developing these models involved extracting femur geometry from clinical CT scans of 62 men and 36 women, fitting a template finite element femur mesh to the surface geometry of each patient, and then programmatically determining thickness at each nodal location. Principal component analysis was then performed on the thickness and geometry nodal coordinates, and linear regression models were developed to predict principal component scores as functions of age, BMI, and femur length. The average absolute errors in male and female external surface geometry model predictions were 4.57 and 4.23 mm, and the average absolute errors in male and female thickness model predictions were 1.67 and 1.74 mm. The average error in midshaft cortical bone areas between the predicted geometries and the patient geometries was 4.4%. The average error in cortical bone area between the predicted geometries and a validation set of cadaver femur geometries across 5 shaft locations was 2.9%.


Principal component analysis Regression Biomechanics Motor-vehicle crashes Lower-extremity injury Subject characteristics 



This project was funded by the National Highway Traffic Safety Administration under Contract Number DTNH22-10-H-00288 and the National Science Foundation under Award Number 1300815. The authors would like to thank Ms. Prabha Narayanaswamy for her support on the statistical analyzes, the University of Virginia Center for Applied Biomechanics for their help in providing the CT scan data, Dr. Johan Ivarsson for providing the CT scan data, and the University of Michigan students who extracted femur geometry.


  1. 1.
    Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control AC. 19:716–723, 1974.CrossRefGoogle Scholar
  2. 2.
    Bennink, H. E., J. M. Korbeeck, B. J. Janssen, and B. M. Ter Haar Romeny. Warping a neuro-anatomy atlas on 3D MRI data with radial basis functions. Proc. Int. Conf. Biomed. Eng. 3:214–218, 2006.Google Scholar
  3. 3.
    Besnault, B., F. Lavaste, H. Guillemot, S. Robin, and J. Y. LeCoz. A parametric finite element model of the human pelvis. Proc. Stapp Car Crash Conf. 42:P337, 1998.Google Scholar
  4. 4.
    Bredbenner, T. L., R. L. Mason, L. M. Havill, E. S. Orwoll, and D. P. Nicolella. Fracture risk predictions based on statistical shape and density modeling of the proximal femur. J. Bone Miner. Res. 29:2090–2100, 2014.CrossRefPubMedPubMedCentralGoogle Scholar
  5. 5.
    Bryan, R., P. S. Mohan, A. Hopkins, F. Galloway, M. Taylor, and P. B. Nair. Statistical modelling of the whole human femur incorporating geometric and material properties. Med. Eng. Phys. 32:57–65, 2010.CrossRefPubMedGoogle Scholar
  6. 6.
    Bryan, R., P. B. Nair, and M. Taylor. Use of a statistical model of the whole femur in a large scale, multi-model study of femoral neck fracture risk. J. Biomech. 42:2171–2176, 2009.CrossRefPubMedGoogle Scholar
  7. 7.
    Carr, J. C., R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans. Reconstruction and representation of 3D objects with radial basis functions. Proc. Annu. Conf. Comput. Gr. Interact. Tech. 28:67–76, 2001.Google Scholar
  8. 8.
    Carter, P. M., C. A. C. Flannagan, M. P. Reed, R. M. Cunningham, and J. D. Rupp. Comparing the effects of age, BMI and gender on severe injury (AIS 3+) in motor-vehicle crashes. Accid. Anal. Prev. 72:146–160, 2014.CrossRefPubMedPubMedCentralGoogle Scholar
  9. 9.
    Clarke, B. Normal bone anatomy and physiology. Clin. J. Am. Soc. Nephrol. 3(Suppl 3):S131–S139, 2008.CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Gayzik, F. S., M. M. Yu, K. A. Danelson, D. E. Slice, and J. D. Stitzel. Quantification of age-related shape change of the human rib cage through geometric morphometrics. J. Biomech. 41:1545–1554, 2008.CrossRefPubMedGoogle Scholar
  11. 11.
    Heaney, R. P. Is the paradigm shifting? Bone 33:457–465, 2003.CrossRefPubMedGoogle Scholar
  12. 12.
    Hu, J., J. D. Rupp, and M. P. Reed. Focusing on vulnerable populations in crashes: recent advances in finite element human models for injury biomechanics research. J. Automot. Saf. Energy 3:295–307, 2012.Google Scholar
  13. 13.
    Ivarsson, B. J., D. Genovese, J. R. Crandall, J. R. Bolton, C. D. Untaroiu, and D. Bose. The tolerance of the femoral shaft in combined axial compression and bending loading. Proc. Stapp Car Crash Conf. 53:251–290, 2009.Google Scholar
  14. 14.
    Joliffe, I. T. Principal Component Analysis. Berlin: Springer, 2002.Google Scholar
  15. 15.
    Keaveny, T. M., P. F. Hoffmann, M. Singh, L. Palermo, J. P. Bilezikian, S. L. Greenspan, and D. M. Black. Femoral bone strength and its relation to cortical and trabecular changes after treatment with PTH, alendronate, and their combination as assessed by finite element analysis of quantitative CT scans. J. Bone Miner. Res. 23:1974–1982, 2008.CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Keyak, J. H., and Y. Falkinstein. Comparison of in situ and in vitro CT scan-based finite element model predictions of proximal femoral fracture load. Med. Eng. Phys. 25:781–787, 2003.CrossRefPubMedGoogle Scholar
  17. 17.
    Kurazume, R., K. Nakamura, T. Okada, Y. Sato, N. Sugano, T. Koyama, Y. Iwashita, and T. Hasegawa. 3D reconstruction of a femoral shape using a parametric model and two 2D fluoroscopic images. Comput. Vis. Image Underst. 113:202–211, 2009.CrossRefGoogle Scholar
  18. 18.
    Li, Z., J. Hu, M. P. Reed, J. D. Rupp, C. N. Hoff, J. Zhang, and B. Cheng. Development, validation, and application of a parametric pediatric head finite element model for impact simulations. Ann. Biomed. Eng. 39:2984–2997, 2011.CrossRefPubMedGoogle Scholar
  19. 19.
    Lu, Y. C., A. R. Kemper, F. S. Gayzik, C. D. Untaroiu, and P. Beillas. Statistical modeling of human liver incorporating the variations in shape, size, and material properties. Proc. Stapp Car Crash Conf. 57:285–311, 2013.Google Scholar
  20. 20.
    Lu, Y. C., and C. D. Untaroiu. Statistical shape analysis of clavicular cortical bone with applications to the development of mean and boundary shape models. Comput. Methods Progr. Biomed. 111:613–628, 2013.CrossRefGoogle Scholar
  21. 21.
    Manary, M. A., M. P. Reed, C. A. C. Flannagan, and L. W. Schneider. ATD positioning based on driver posture and position. Proc. Stapp Car Crash Conf. 42:P-337, 1998.Google Scholar
  22. 22.
    Moran, S. G., G. McGwin, Jr., J. S. Metzger, J. E. Alonso, and L. W. Rue, 3rd. Relationship between age and lower extremity fractures in frontal motor vehicle collisions. J. Trauma 54:261–265, 2003.CrossRefPubMedGoogle Scholar
  23. 23.
    Nalla, R. K., J. J. Kruzic, J. H. Kinney, and R. O. Ritchie. Effect of aging on the toughness of human cortical bone: evaluation by R-curves. Bone 35:1240–1246, 2004.CrossRefPubMedGoogle Scholar
  24. 24.
    Nicolella, D. P., and T. L. Bredbenner. Development of a parametric finite element model of the proximal femur using statistical shape and density modeling. Comput. Methods Biomech. Biomed. Eng. 15:101–110, 2012.CrossRefGoogle Scholar
  25. 25.
    Park, B. K., J. C. Lumeng, C. N. Lumeng, S. M. Ebert, and M. P. Reed. Child body shape measurement using depth cameras and a statistical body shape model. Ergonomics 58:301–309, 2015.CrossRefPubMedGoogle Scholar
  26. 26.
    Reed, M. P., S. M. Ebert, and J. J. Hallman. Effects of driver characteristics on seat belt fit. Proc. Stapp Car Crash Conf. 57:43–57, 2013.Google Scholar
  27. 27.
    Reed, M. P., and M. B. Parkinson. Modeling variability in torso shape for chair and seat design. Proc. ASME Design Eng. Tech. Conf. 1:562–570, 2008.Google Scholar
  28. 28.
    Reed, M. P., M. M. Sochor, J. D. Rupp, K. D. Klinich, and M. A. Manary. Anthropometric specification of child crash dummy pelves through statistical analysis of skeletal geometry. J. Biomech. 42:1143–1145, 2009.CrossRefPubMedGoogle Scholar
  29. 29.
    Ridella, S. A., A. Beyersmith, and K. Poland. Factors associated with age-related differences in crash injury types, causation, and mechanisms. In: Proceedings of Emerging Issues in Safe and Sustainable Mobility for Older Persons TRB ANB60 Fall 2011 Conference, Washington, DC, 2011.Google Scholar
  30. 30.
    Rupp, J. D., and C. A. C. Flannagan. Effects of occupant age on AIS 3 + injury outcome determined from analyses of fused NASS/CIREN data. In: SAE 2011 Government/Industry Meeting, Washington, DC, 2011.Google Scholar
  31. 31.
    Shi, X., L. Cao, M. P. Reed, J. D. Rupp, C. N. Hoff, and J. Hu. A statistical human rib cage geometry model accounting for variations by age, sex, stature and body mass index. J. Biomech. 47:2277–2285, 2014.CrossRefPubMedGoogle Scholar
  32. 32.
    Slice, D. E. Geometric morphometrics. Annu. Rev. Anthropol. 36:261–281, 2007.CrossRefGoogle Scholar
  33. 33.
    Toyota Motor Corporation. THUMS AM50 pedestrian/occupant model academic version 4.0, 2011.Google Scholar

Copyright information

© Biomedical Engineering Society 2015

Authors and Affiliations

  • Katelyn F. Klein
    • 1
    • 2
  • Jingwen Hu
    • 1
  • Matthew P. Reed
    • 1
    • 3
  • Carrie N. Hoff
    • 4
  • Jonathan D. Rupp
    • 1
    • 2
    • 5
  1. 1.University of Michigan Transportation Research InstituteUniversity of MichiganAnn ArborUSA
  2. 2.Department of Biomedical EngineeringUniversity of MichiganAnn ArborUSA
  3. 3.Department of Industrial and Operations EngineeringUniversity of MichiganAnn ArborUSA
  4. 4.Department of RadiologyUniversity of MichiganAnn ArborUSA
  5. 5.Department of Emergency MedicineUniversity of MichiganAnn ArborUSA

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