Abstract
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 develo** 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%.
Similar content being viewed by others
References
Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control AC. 19:716–723, 1974.
Bennink, H. E., J. M. Korbeeck, B. J. Janssen, and B. M. Ter Haar Romeny. War** a neuro-anatomy atlas on 3D MRI data with radial basis functions. Proc. Int. Conf. Biomed. Eng. 3:214–218, 2006.
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.
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.
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.
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.
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.
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.
Clarke, B. Normal bone anatomy and physiology. Clin. J. Am. Soc. Nephrol. 3(Suppl 3):S131–S139, 2008.
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.
Heaney, R. P. Is the paradigm shifting? Bone 33:457–465, 2003.
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.
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.
Joliffe, I. T. Principal Component Analysis. Berlin: Springer, 2002.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Slice, D. E. Geometric morphometrics. Annu. Rev. Anthropol. 36:261–281, 2007.
Toyota Motor Corporation. THUMS AM50 pedestrian/occupant model academic version 4.0, 2011.
Acknowledgments
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Associate Editor Stefan M Duma oversaw the review of this article.
Rights and permissions
About this article
Cite this article
Klein, K.F., Hu, J., Reed, M.P. et al. Development and Validation of Statistical Models of Femur Geometry for Use with Parametric Finite Element Models. Ann Biomed Eng 43, 2503–2514 (2015). https://doi.org/10.1007/s10439-015-1307-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10439-015-1307-6