Department of Applied Mechanics, CEIT-IK4, TECNUN, Manuel Lardizabal 15, San Sebastia´n 20018, Spain.
IEEE Trans Vis Comput Graph. 2012 Feb;18(2):228-41. doi: 10.1109/TVCG.2011.32.
Mass-Spring Models (MSMs) are used to simulate the mechanical behavior of deformable bodies such as soft tissues in medical applications. Although they are fast to compute, they lack accuracy and their design remains still a great challenge. The major difficulties in building realistic MSMs lie on the spring stiffness estimation and the topology identification. In this work, the mechanical behavior of MSMs under tensile loads is analyzed before studying the spring stiffness estimation. In particular, the performed qualitative and quantitative analysis of the behavior of cubical MSMs shows that they have a nonlinear response similar to hyperelastic material models. According to this behavior, a new method for spring stiffness estimation valid for linear and nonlinear material models is proposed. This method adjusts the stress-strain and compressibility curves to a given reference behavior. The accuracy of the MSMs designed with this method is tested taking as reference some soft-tissue simulations based on nonlinear Finite Element Method (FEM). The obtained results show that MSMs can be designed to realistically model the behavior of hyperelastic materials such as soft tissues and can become an interesting alternative to other approaches such as nonlinear FEM.
质量-弹簧模型（MSM）用于模拟可变形体的机械行为，例如医学应用中的软组织。虽然它们计算速度很快，但准确性却缺乏，其设计仍然是一个巨大的挑战。构建逼真的 MSM 的主要困难在于弹簧刚度估计和拓扑识别。在研究弹簧刚度估计之前，本工作分析了拉伸载荷下 MSM 的力学行为。特别是，对立方 MSM 行为的定性和定量分析表明，它们具有类似于超弹性材料模型的非线性响应。根据这种行为，提出了一种新的弹簧刚度估计方法，适用于线性和非线性材料模型。该方法将应力-应变和可压缩性曲线调整为给定的参考行为。使用该方法设计的 MSM 的准确性通过基于非线性有限元方法（FEM）的一些软组织模拟作为参考进行了测试。所得结果表明，可以设计 MSM 以真实地模拟超弹性材料（例如软组织）的行为，并且可以成为其他方法（例如非线性 FEM）的有趣替代方法。
