Relaxation Young’s modulus of cortical bone was investigated for two different directions with respect to the longitudinal axis of bone (bone axis, BA):​ the modulus parallel (P) and normal (N) to the BA. The relaxation modulus was analyzed by fitting to the empirical equation previously proposed for cortical bones, i.e., a linear combination of two Kohlraush–Williams–Watts (KWW) functions (Iyo et al., 2003. Biorheology, submitted):​

[equation]

where E₀ is the initial modulus value E(0). τ₁ and τ₂(⪢τ₁)are characteristic times of the relaxation, A1 is the fractional contribution of the fast relaxation (KWW1 process) to the whole relaxation process, and β and γ are parameters describing the shape of the relaxation modulus. In both P and N samples, the relaxation modulus was described well by the empirical equation. The KWW1 process of a P sample almost completely coincided with that of an N sample. In the slow process (KWW2 process), there was a difference between the relaxation modulus of a P sample and that of an N sample. The results indicate that the KWW1 process in the empirical equation represents the relaxation in the collagen matrix in bone and that the KWW2 process is related to a higher-order structure of bone that is responsible for the anisotropic mechanical properties of bone.