Grant J W, Cotton J R
Engineering Science and Mechanics Department, Virginia Polytechnic Institute and State University, Blacksburg 24061-0219.
J Vestib Res. 1990;1(2):139-51.
The otolith organs were modeled mathematically as a 3-element system consisting of a viscous endolymph fluid in contact with a rigid otoconial layer that is attached to the skull by a gel layer. The gel layer was considered to be viscoelastic solid, and was modeled as a simple Kelvin material. The governing differential equations of motion were derived and nondimensionalized, yielding 3 nondimensional parameters: nondimensional density, nondimensional viscosity, and nondimensional elasticity. The equations were solved using finite difference techniques on a digital computer. By comparing the model's response with previous experimental research, values for the nondimensional parameters were found. The results indicate that the inclusion of viscous and elastic effects in the gel layer are necessary for the model to produce otoconial layer deflections that are consistent with physiologic displacements. Future experimental data analysis and mathematical modeling effects should include viscoelastic gel layer effects, as this is a major contributor to system damping and response.
耳石器官被数学建模为一个由三部分组成的系统，该系统包括与刚性耳石层接触的粘性内淋巴液，耳石层通过凝胶层附着于颅骨。凝胶层被视为粘弹性固体，并被建模为简单的开尔文材料。推导并对运动控制微分方程进行无量纲化处理，得出三个无量纲参数：无量纲密度、无量纲粘度和无量纲弹性。使用数字计算机上的有限差分技术求解这些方程。通过将模型的响应与先前的实验研究进行比较，得出无量纲参数的值。结果表明，凝胶层中粘性和弹性效应的纳入对于模型产生与生理位移一致的耳石层偏转是必要的。未来的实验数据分析和数学建模效应应包括粘弹性凝胶层效应，因为这是系统阻尼和响应的主要贡献因素。
