The anisotropy of Young's modulus in human cortical bone was determined for
all spatial directions by performing coordinate rotations of a 6 by 6 elas
tic stiffness matrix. The elastic stiffness coefficients were determined ex
perimentally from ultrasonic velocity measurements on 96 samples of normal
cortical bone removed from the right tibia of eight human cadavers. The fol
lowing measured values were used for our analysis: c(11) = 19.5 GPa, c(22)
= 20.1 GPa, c(33) = 30.9 GPa, c(44) = 5.72 GPa, c(55) = 5.17 GPa, c(66) = 4
.05 GPa, c(23) = 12.5 GPa. The remaining coefficients were determined by as
suming that the specimens possessed at least an orthorhombic elastic symmet
ry, and further assuming that c(13) = c(23) c(12) = c(11) - 2c(66). Our ana
lysis revealed a substantial anisotropy in Young's modulus in the plane con
taining the long axis of the tibia, with maxima of 20.9 GPa parallel to the
long axis, and minima of 11.8 GPa perpendicular to this axis. A less prono
unced anisotropy was observed in the plane perpendicular to the long axis o
f the tibia. To display our results for the full three-dimensional anisotro
py of cortical bone, a closed surface was used to represent Young's modulus
in all spatial directions.