Department of Orthopaedics and Rehabilitation, University of Vermont, Stafford Hall, Burlington, VT 05405-0084, USA.
Ann Biomed Eng. 2011 Jan;39(1):122-31. doi: 10.1007/s10439-010-0140-1. Epub 2010 Aug 14.
Intervertebral disks support compressive forces because of their elastic stiffness as well as the fluid pressures resulting from poroelasticity and the osmotic (swelling) effects. Analytical methods can quantify the relative contributions, but only if correct material properties are used. To identify appropriate tissue properties, an experimental study and finite element analytical simulation of poroelastic and osmotic behavior of intervertebral disks were combined to refine published values of disk and endplate properties to optimize model fit to experimental data. Experimentally, nine human intervertebral disks with adjacent hemi-vertebrae were immersed sequentially in saline baths having concentrations of 0.015, 0.15, and 1.5 M and the loss of compressive force at constant height (force relaxation) was recorded over several hours after equilibration to a 300-N compressive force. Amplitude and time constant terms in exponential force-time curve-fits for experimental and finite element analytical simulations were compared. These experiments and finite element analyses provided data dependent on poroelastic and osmotic properties of the disk tissues. The sensitivities of the model to alterations in tissue material properties were used to obtain refined values of five key material parameters. The relaxation of the force in the three bath concentrations was exponential in form, expressed as mean compressive force loss of 48.7, 55.0, and 140 N, respectively, with time constants of 1.73, 2.78, and 3.40 h. This behavior was analytically well represented by a model having poroelastic and osmotic tissue properties with published tissue properties adjusted by multiplying factors between 0.55 and 2.6. Force relaxation and time constants from the analytical simulations were most sensitive to values of fixed charge density and endplate porosity.
椎间盘具有弹性刚度，并且由于多孔弹性和渗透（膨胀）作用会产生流体压力，因此能够支撑压缩力。分析方法可以定量分析相对贡献，但前提是使用正确的材料特性。为了确定合适的组织特性，将椎间盘的多孔弹性和渗透行为的实验研究和有限元分析模拟相结合，以细化已发表的椎间盘和终板特性值，从而使模型更好地拟合实验数据。在实验中，将 9 个人椎间盘及其相邻的半个椎体依次浸入盐浴中，盐浴浓度分别为 0.015、0.15 和 1.5 M，在平衡至 300 N 的压缩力后数小时内记录恒定高度下的压缩力损失（力松弛）。比较了实验和有限元分析模拟中指数力-时间曲线拟合的幅度和时间常数项。这些实验和有限元分析提供了依赖于椎间盘组织多孔弹性和渗透特性的数据。模型对组织材料特性变化的敏感性用于获得五个关键材料参数的细化值。在三种浴浓度下，力的松弛呈指数形式，分别表示为平均压缩力损失 48.7、55.0 和 140 N，时间常数分别为 1.73、2.78 和 3.40 h。该行为由具有多孔弹性和渗透组织特性的模型很好地表示，已发表的组织特性通过乘以 0.55 至 2.6 之间的因子进行了调整。分析模拟的力松弛和时间常数对固定电荷密度和终板孔隙率的数值最为敏感。
