Guilkey James E, Hoying James B, Weiss Jeffrey A
Department of Mechanical Engineering, The University of Utah, 50 South Central Campus Drive, Room 2202, Salt Lake City, Utah 84112, USA.
J Biomech. 2006;39(11):2074-86. doi: 10.1016/j.jbiomech.2005.06.017. Epub 2005 Aug 10.
Computational modeling of the mechanics of cells and multicellular constructs with standard numerical discretization techniques such as the finite element (FE) method is complicated by the complex geometry, material properties and boundary conditions that are associated with such systems. The objectives of this research were to apply the material point method (MPM), a meshless method, to the modeling of vascularized constructs by adapting the algorithm to accurately handle quasi-static, large deformation mechanics, and to apply the modified MPM algorithm to large-scale simulations using a discretization that was obtained directly from volumetric confocal image data. The standard implicit time integration algorithm for MPM was modified to allow the background computational grid to remain fixed with respect to the spatial distribution of material points during the analysis. This algorithm was used to simulate the 3D mechanics of a vascularized scaffold under tension, consisting of growing microvascular fragments embedded in a collagen gel, by discretizing the construct with over 13.6 million material points. Baseline 3D simulations demonstrated that the modified MPM algorithm was both more accurate and more robust than the standard MPM algorithm. Scaling studies demonstrated the ability of the parallel code to scale to 200 processors. Optimal discretization was established for the simulations of the mechanics of vascularized scaffolds by examining stress distributions and reaction forces. Sensitivity studies demonstrated that the reaction force during simulated extension was highly sensitive to the modulus of the microvessels, despite the fact that they comprised only 10.4% of the volume of the total sample. In contrast, the reaction force was relatively insensitive to the effective Poisson's ratio of the entire sample. These results suggest that the MPM simulations could form the basis for estimating the modulus of the embedded microvessels through a parameter estimation scheme. Because of the generality and robustness of the modified MPM algorithm, the relative ease of generating spatial discretizations from volumetric image data, and the ability of the parallel computational implementation to scale to large processor counts, it is anticipated that this modeling approach may be extended to many other applications, including the analysis of other multicellular constructs and investigations of cell mechanics.
利用有限元（FE）方法等标准数值离散技术对细胞和多细胞构建体的力学进行计算建模，会因与此类系统相关的复杂几何形状、材料特性和边界条件而变得复杂。本研究的目标是将无网格的物质点法（MPM）应用于血管化构建体的建模，通过调整算法来精确处理准静态、大变形力学，并将改进的MPM算法应用于使用直接从体积共聚焦图像数据获得的离散化进行的大规模模拟。对MPM的标准隐式时间积分算法进行了修改，以使背景计算网格在分析过程中相对于物质点的空间分布保持固定。该算法用于通过用超过1360万个物质点对构建体进行离散化，来模拟在张力作用下由嵌入胶原凝胶中的生长微血管片段组成的血管化支架的三维力学。基线三维模拟表明，改进的MPM算法比标准MPM算法更准确、更稳健。缩放研究表明并行代码能够扩展到200个处理器。通过检查应力分布和反作用力，为血管化支架力学模拟建立了最佳离散化。敏感性研究表明，尽管微血管仅占总样本体积的10.4%，但模拟伸展过程中的反作用力对微血管的模量高度敏感。相比之下，反作用力对整个样本的有效泊松比相对不敏感。这些结果表明，MPM模拟可为通过参数估计方案估算嵌入微血管的模量奠定基础。由于改进的MPM算法的通用性和稳健性、从体积图像数据生成空间离散化相对容易，以及并行计算实现能够扩展到大量处理器，预计这种建模方法可能会扩展到许多其他应用，包括分析其他多细胞构建体和研究细胞力学。
