Zhang Wei, Chen Henry Y, Kassab Ghassan S
Department of Biomedical Engineering, IUPUI, Indianapolis, IN 46202, USA.
Biomaterials. 2007 Aug;28(24):3579-86. doi: 10.1016/j.biomaterials.2007.04.040. Epub 2007 May 5.
It is well known that many biological soft tissues behave as viscoelastic materials with hysteresis curves being nearly independent of strain rate when loading frequency is varied over a large range. In this work, the rate-insensitive feature of biological materials is taken into account by a generalized Maxwell model. To minimize the number of model parameters, it is assumed that the characteristic frequencies of Maxwell elements form a geometric series. As a result, the model is characterized by five material constants: micro(0), tau, m, rho and beta, where micro(0) is the relaxed elastic modulus, tau the characteristic relaxation time, m the number of Maxwell elements, rho the gap between characteristic frequencies, and beta=micro(1)/micro(0) with micro(1) being the elastic modulus of the Maxwell body that has relaxation time tau. The physical basis of the model is motivated by the microstructural architecture of typical soft tissues. The novel model shows excellent fit of relaxation data on the canine aorta and captures the salient features of vascular viscoelasticity with significantly fewer model parameters.
众所周知，许多生物软组织表现为粘弹性材料，当加载频率在很大范围内变化时，滞后曲线几乎与应变率无关。在这项工作中，通过广义麦克斯韦模型考虑了生物材料的速率不敏感特性。为了最小化模型参数的数量，假设麦克斯韦元件的特征频率形成几何级数。结果，该模型由五个材料常数表征：μ(0)、τ、m、ρ和β，其中μ(0)是松弛弹性模量，τ是特征松弛时间，m是麦克斯韦元件的数量，ρ是特征频率之间的间隔，β = μ(1)/μ(0)，其中μ(1)是具有松弛时间τ的麦克斯韦体的弹性模量。该模型的物理基础是由典型软组织的微观结构架构激发的。该新型模型对犬主动脉的松弛数据显示出极好的拟合，并以明显更少的模型参数捕捉了血管粘弹性的显著特征。
