Numerical Simulation of Anisotropic Tissue Growth Using a Total Lagrangian Formulation
Numerical Simulation of Anisotropic Tissue Growth Using a Total Lagrangian Formulation
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DOI：
10.1155/2015/674639
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发表时间：
2015-02
影响因子：
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通讯作者：
G. Joldes;Benjamin F. Zwick
中科院分区：
文献类型：
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作者：
G. Joldes;Benjamin F. Zwick
本文描述了一种模拟组织生长的新方法，可以处理体积的各向异性变化。该方法利用了总拉格朗日公式，该公式允许基于理论无应力配置计算有限元网格中每个单元的节点力，该配置是通过考虑所考虑单元的无约束各向异性增长而获得的。该方法允许对收缩（萎缩）、肿胀或组织生长进行建模，并计算周围组织中产生的机械应力。使用显式积分方法和动态松弛获得稳态解。所提出的方法允许将连续力学模拟与潜在的生长机制耦合，为组织生长的多尺度研究提供了工具。
This paper describes a new method for simulating tissue growth which can handle anisotropic changes in volume. The method takes advantage of the total Lagrangian formulation which allows the computation of nodal forces for each element in a finite element mesh based on a theoretical stress-free configuration, obtained by considering the unconstrained anisotropic growth of the considered element. The method allows the modelling of shrinking (atrophy), swelling, or tissue growth and the computation of the resulting mechanical stresses in the surrounding tissue. The steady-state solution is obtained using an explicit integration method and dynamic relaxation. The proposed method allows the coupling of continuum mechanical simulations with underlying growth mechanisms, offering a tool for the multiscale study of tissue growth.