Fractional order viscoelasticity of the aortic valve cusp: An alternative to quasilinear viscoelasticity
Fractional order viscoelasticity of the aortic valve cusp: An alternative to quasilinear viscoelasticity
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DOI：
10.1115/1.1933900
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发表时间：
2005-08-01
影响因子：
1.7
通讯作者：
Vesely, I
中科院分区：
文献类型：
--
作者：
Doehring, TC;Freed, AD;Vesely, I
背景资料：准线性粘弹性（QLV）理论已被广泛和成功地用于描述结缔组织的时间相关响应。然而，困难仍然存在，特别是在材料参数估计和灵敏度。在这项研究中，我们引入了一个新的替代方案：分数阶粘弹性（FOV）理论，它使用分数阶积分来描述松弛响应。FOV意味着分形样组织结构，反映了胶原组织的分级排列。接近方法：开发了一维（I-D）FOV简化弛豫函数，用分数弛豫函数代替QLV“箱谱”函数。采用直接拟合、全局优化方法，从主动脉瓣组织的应力松弛试验中估计材料参数。结果如下：我们发现，对于主动脉心脏瓣膜，FOV具有类似的准确性和更好的参数灵敏度比QLV，特别是对于长时间常数（tau 2）。平均（n = 5）分数阶为0.29，表明组织的粘弹性响应是强烈的分形样。结果总结：平均QLV参数为C = 0.079，tau 1 = 0.004，tau 2 = 76，平均FOV参数为8 = 0.29，r = 0.076，p = 1.84。结论：FOV可以提供有价值的新的见解组织粘弹性行为。确定分数阶可以为组织比较提供新的和灵敏的定量测量。
Background: Quasilinear viscoelasticity (QLV) theory has been widely and successfully used to describe the time-dependent response of connective tissues. Difficulties remain, however particularly in material parameter estimation and sensitivities. In this study, we introduce a new alternative: the fractional order viscoelasticity (FOV) theory, which uses a fractional order integral to describe the relaxation response. FOV implies a fractal-like tissue structure, reflecting the hierarchical arrangement of collagenous tissues. Method of Approach: A one-dimensional (I-D) FOV reduced relaxation function was developed, replacing the QLV "box-spectrum" function with a fractional relaxation function. A direct-fit, global optimization method was used, to estimate material parameters from stress relaxation tests on aortic valve tissue. Results: We found that for the aortic heart valve, FOV had similar accuracy and better parameter sensitivity than QLV particularly for the long time constant (tau 2). The mean (n = 5) fractional order was 0.29, indicating that the viscoelastic response of the tissue was strongly fractal-like. Results summary: mean QLV parameters were C = 0.079, tau 1 = 0.004, tau 2 = 76, and mean FOV parameters were 8 = 0.29, r = 0.076, and p = 1.84. Conclusions: FOV can provide valuable new in-sights into tissue viscoelastic behavior. Determining the fractional order can provide a new and sensitive quantitative measure for tissue comparison.