A minimal parametric model of the femur to describe axial elastic strain in response to loads

L. Cristofolini, Angelo Cappello, B. P. McNamara, M. Viceconti

Research output: Contribution to journalArticlepeer-review


Evaluating the state of stress/strain for a given geometry and load in femurs can be done both experimentally, measuring strain at a limited number of locations, and theoretically with finite element models. Another approach is to describe the state of strain with a few synthetic indices. For this purpose the reverse elastic problem (i.e. bone parameters are estimated given the strain distribution and loads) needs to be solved as opposed to the finite element direct problem. Such reverse models can be then used: (1) to describe simply the strain distribution by means of few synthetic indices; (2) to explain the state of strain; and (3) to predict the strain distribution under different loading conditions. Various linear models, characterized by two to five bone-related parameters, were tested on (1) 12 femurs, (2) a finite element model, and (3) data taken from the literature, for a total of 43 loading cases. Three- and four-parameter models were able to fit the experimental strain distributions with mean squared residuals smaller than 5% of the strain range. The consistency of the model was proved by the repeatability of the parameters estimate for identical femurs. Furthermore, the bone-related coefficients were able to detect the stiffening effect of the implantation of an uncemented stem. Finally, the model can be used for predictive pruposes if the parameter estimates are used with different loading conditions.

Original languageEnglish
Pages (from-to)502-514
Number of pages13
JournalMedical Engineering and Physics
Issue number6
Publication statusPublished - Sep 1996


  • Beam theory
  • Diaphysis
  • Human femur
  • Model
  • Strain

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine
  • Psychology(all)


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