Modeling the Intervertebral Discs as a Stiffness Matrix: a SpineBushing element

This project features a "SpineBushing" element that can be used to model the intervertebral disc as a 6x6 stiffness matrix. This permits the study of the disc's force-motion relationship for the case where the coordinates are coupled to each other. The guiding equation is,F_2 = -K * Delta_Qwhere F_2 is the generalized 6x1 force vector acting on the upper vertebra, K is a stiffness matrix, and Delta_Q is the generalized 6x1 displacement vector specifying the change in position from neutral between the points of attachment of the stiffness element.By Newton's 3rd law, F_1 = - F_2.The SpineBushing features two *key* differences from the existing bushing element:(1) we incorporated a full 6x6 stiffness matrix instead of the current three translational and three rotational stiffnesses.(2) the **change** in relative motion is used and not the relative motion itself. In 1-D, you can think of this as having a spring with a resting length equal to the distance between the specified attachment points on the two bodies in the neutral posture. (The typical bushing element, on the other hand would be analogous to a spring with zero resting length.)Further details are provided in the accompanying documents. <br/><br/>This project includes the following software/data packages: <br/> <ul> <li> <a href="https://simtk.org/frs?group_id=687#pack_1124">Model and CMC Files </a> : Contains OpenSimm model files, and a ton of other files necessary for running CMC. Further details given in the readme document. Maurice is pretty much the CMC-pro here (I'm just the one with the cow on my shoulder), so 100% of the credit goes to him for managing to get CMC to work. Even if you're not planning on running CMC, give his readme document a read-through. I guarantee you'll learn something. </li> <li> <a href="https://simtk.org/frs?group_id=687#pack_1121">Source Code </a> : Source Code for building the SpineBushing plugin </li> </ul>

本项研究特色在于引入了一种名为“椎间板”的元素，该元素可用于模拟椎间盘作为6x6刚度矩阵。此举使得研究者能够探究在坐标相互耦合的情况下，椎间盘的力-位移关系。指导方程为：F_2 = -K * Delta_Q，其中F_2是作用于上位椎骨的广义6x1力向量，K为刚度矩阵，Delta_Q为广义6x1位移向量，用于指定刚度元件附着点之间从中性位置的变化。根据牛顿第三定律，F_1 = - F_2。椎间板与现有的衬套元件相比，具有两大关键差异：（1）我们采用了完整的6x6刚度矩阵，而非当前的三种平移和三种旋转刚度；（2）使用的是相对运动的**变化**而非相对运动本身。在一维情况下，可以将其视为具有与两个物体在中性姿态下指定附着点之间距离相等的静态长度的弹簧（而典型的衬套元件则类似于静态长度为零的弹簧）。伴随的详细资料可在附带的文件中获得。本项目中包含以下软件/数据包：（1）<a href="https://simtk.org/frs?group_id=687#pack_1124">模型和CMC文件</a>：包含OpenSimm模型文件以及运行CMC所需的大量其他文件。详情请参阅readme文档。Maurice是CMC的专家（而我只是那个肩上有牛的人），因此，将CMC成功运行的所有功劳都归功于他。即使您不打算运行CMC，也请阅读他的readme文档，我保证您会有所收获。（2）<a href="https://simtk.org/frs?group_id=687#pack_1121">源代码</a>：构建椎间板插件的源代码。