Department of Biomedical Engineering, The Ohio State University, Columbus, OH, United States.
Department of Biomedical Engineering, West Virginia University, Morgantown, WV, United States.
J Biomech. 2024 Feb;164:111965. doi: 10.1016/j.jbiomech.2024.111965. Epub 2024 Feb 3.
Nucleus pulposus (NP) tissue in the intervertebral disc (IVD) is a viscoelastic material exhibiting both solid- and fluid-like mechanical behaviors. Advances in viscoelastic models incorporating fractional calculus, such as the Fractional Zener (FZ) model, have potential to describe viscoelastic behaviors. The objectives of this study were to determine whether the FZ model can accurately describe the shear viscoelastic properties of NP tissue and determine if the fractional order (α) is related to tissue hydration. 30 caudal IVDs underwent equilibrium dialysis in 5% or 25% polyethylene glycol solutions to alter tissue hydration. Excised NP tissue underwent stress relaxation testing in shear and unconfined compression. Stress relaxation data was fitted to the FZ model to obtain viscoelastic properties. In both loading modes, the initial modulus was greater for the less hydrated 25% equilibrated samples compared to 5% with no change in the equilibrium modulus. Samples with lower water content (25% samples) had shorter relaxation times in shear and longer time constants in compression, highlighting the different interactions between the fluid and solid matrix in loading modes. Samples with lower water content had α values closer to 0, indicating that less hydrated samples behaved more solid-like on the viscoelastic spectrum. Tissue hydration correlated with α values for 25% samples in shear. This study demonstrates that the FZ model may be used to describe IVD tissue behavior under both loading modes; however, the greatest utility of the FZ model is in describing flow-independent shear behaviors, and α may inform tissue hydration in shear.
椎间盘（IVD）内的髓核（NP）组织是一种黏弹性材料，表现出固态和液态力学行为。采用分数微积分的黏弹性模型（如分数泽纳（FZ）模型）的进步具有描述黏弹性行为的潜力。本研究的目的是确定 FZ 模型是否可以准确描述 NP 组织的剪切黏弹性特性，以及分数阶（α）是否与组织水合作用有关。30 个尾骨 IVD 在 5%或 25%聚乙二醇溶液中进行平衡透析以改变组织水合作用。切除的 NP 组织在剪切和无约束压缩下进行应力松弛测试。将应力松弛数据拟合到 FZ 模型以获得黏弹性特性。在两种加载模式下，初始模量对于水合作用较低的 25%平衡样品比对 5%未平衡样品更高，而平衡模量没有变化。含水量较低的样品（25%的样品）在剪切中的松弛时间较短，在压缩中的时间常数较长，这突出了在加载模式下流体和固体基质之间的不同相互作用。含水量较低的样品的α值更接近 0，这表明水合作用较低的样品在黏弹性谱上表现出更固态的行为。组织水合作用与 25%样品在剪切中的α值相关。本研究表明，FZ 模型可用于描述两种加载模式下的 IVD 组织行为；然而，FZ 模型的最大用途是描述独立于流动的剪切行为，并且α可能在剪切中反映组织水合作用。
