TY - JOUR

T1 - Anisotropic viscoelastic properties of cortical bone

AU - Iyo, Toshiya

AU - Maki, Yasuyuki

AU - Sasaki, Naoki

AU - Nakata, Mitsuo

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2004/9

Y1 - 2004/9

N2 - 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):E(t)=E0{A 1 exp[-(t/τ1)β]+(1-A1) exp[-(t/τ2)γ]},[0<A1,β, γ<1],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.

AB - 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):E(t)=E0{A 1 exp[-(t/τ1)β]+(1-A1) exp[-(t/τ2)γ]},[0<A1,β, γ<1],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.

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U2 - 10.1016/j.jbiomech.2003.12.023

DO - 10.1016/j.jbiomech.2003.12.023

M3 - Article

C2 - 15275852

AN - SCOPUS:3242741106

VL - 37

SP - 1433

EP - 1437

JO - Journal of Biomechanics

JF - Journal of Biomechanics

SN - 0021-9290

IS - 9

ER -