Research on Constitutive Laws of Lumbar Intervertebral Disc with Biphasic Thoery

本研究的目的是应用双相理论建立腰椎间盘的本构关系，并利用计算力学模拟椎间盘的粘弹性变形。（1）为了对腰椎间盘的粘弹性变形进行力学分析，根据两相理论建立了本构方程，并提出了一种能反映椎间盘内部组织（髓核、纤维环及其过渡区）力学行为的建模方法。采用有限元方法的计算分析可以模拟椎间盘的蠕变变形，并考虑时间依赖性。(2)利用小牛腰椎节段（两个椎体和一个椎间盘）建立了低频振动载荷下椎间盘内压力响应的测量方法。实验在生理盐水溶液中进行，以模拟体内条件。在振动试验之前，在1小时内在恒定载荷下测量平衡压力。在椎间盘内压力达到平衡后，控制振幅和频率。(3)用有限变形理论对腰椎间盘的宏观本构关系进行了数学描述。通过对尸体腰椎间盘进行连续循环压缩-拉伸实验和连续循环轴向扭转实验，得到了其力学行为。这些方程考虑了髓核或不考虑髓核。还证实，可以从这些方程数值模拟盘的前后弯曲行为。

The aim of this research project is to develop the constitutive laws of lumbar intervertebral discs by applying the biphasic theory, and to simulate the visco-elastic deformation of the disc using the computational mechanics. The following results were obtained :(1) To analyze mechanically the visco-elastic deformation of the lumbar intervertebral disc, the constitutive equations were formulated from by the biphasic theory, and was developed a modeling method represented the mechanical behavior of inner tissues in the disc : nucleus pulposus, annulus fibrosus and the trangeint region between them. The computational analysis using the finite element method could simulate the creep deformation of the intervertebral disc taking time dependency into account.(2) The method to measure the intradiscal pressure response to low-frequency vibration loading was developed using a calf lumbar spinal segment which is two vertebral bodies and one intervertebral disc. The experiment was carried out in a physiological saline solution to simulate in vivo conditions. Prior to the vibration test, the equilibrium pressure was measured under the constant load during I hour. The amplitude and frequency were controlled after the intradiscal pressure reached the equilibrium.(3) The macroscopic constitutive law of the lumbar intervertebral disc to be described mathematically with the finite deformation theory. Mechanical behaviors of the cadaveric lumbar disc obtained from continuous cyclic compression-tension test and continuous cyclic axial torsion test were formulated by the constitutive equation with a semi-circular shaped model. These equations were taken with or without nucleus pulposus into account. It was also confirmed that forward-backward bending behavior of the disc could be simulated numerically from these equations.