Analyzing the anisotropic Hooke׳s law for children׳s cortical bone

  • Lefèvre Emmanuelle
  • Lasaygues Philippe
  • Baron Cécile
  • Payan Cédric
  • Launay Franck
  • Follet Hélène
  • Pithioux Martine


Child cortical bone tissue is rarely studied because of the difficulty of obtaining samples. Yet the preparation and ultrasonic characterization of the small samples available, while challenging, is one of the most promising ways of obtaining information on the mechanical behavior of non-pathological children׳s bone. We investigated children׳s cortical bone obtained from chirurgical waste. 22 fibula or femur samples from 21 children (1–18 years old, mean age: 9.7±5.8 years old) were compared to 16 fibula samples from 16 elderly patients (50–95 years old, mean age: 76.2±13.5 years old). Stiffness coefficients were evaluated via an ultrasonic method and anisotropy ratios were calculated as the ratio of C33/C11, C33/C22 and C11/C22. Stiffness coefficients were highly correlated with age in children (R>0.56, p<0.01). No significant difference was found between \{C11\} and \{C22\} for either adult or child bone (p>0.5), nor between \{C44\} and \{C55\} (p>0.5). We observe a transverse isotropy with C33>C22=C11>C44C55>C66. For both groups, we found no correlation between age and anisotropy ratios. This study offers the first complete analysis of stiffness coefficients in the three orthogonal bone axes in children, giving some indication of how bone anisotropy is related to age. Future perspectives include studying the effect of the structure and composition of bone on its mechanical behavior.