On the theory of reactive mixtures for modeling biological growth
On the theory of reactive mixtures for modeling biological growth
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DOI：
10.1007/s10237-006-0070-x
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发表时间：
2007-11-01
影响因子：
3.5
通讯作者：
Ateshian, Gerard A.
中科院分区：
文献类型：
--
作者：
Ateshian, Gerard A.
混合物理论将联合收割机的固体和流体的运动和变形的连续理论与化学的一般原理相结合，非常适合于模拟生物组织的复杂响应，包括组织生长和重塑、组织工程、细胞的机械生物学和各种其他活性过程。在生物力学文献中缺乏对带电固体和流体成分的反应混合物的方程的全面介绍。本文给出了由受约束的固体混合物和多种流体组成的反应混合物的守恒定律和熵不等式，以及界面跳跃条件。这些成分本质上是不可压缩的，并且可以携带电荷。的界面跳跃条件的质量通量的各个组成部分被示出定义的表面生长方程，它预测沉积或去除的固体基质中的材料点，补充描述的体积增长所描述的质量守恒。提出了一种物质点集随时间变化的物体的参考位形公式。状态变量的定义，可以占固体基质体积的增长和重塑。本构约束的应力和动量供应的各种成分，以及界面跳跃条件的电化学电位的流体。适当的生物组织的简化也提出了，这有助于减少到一个更实用的格式的控制方程。结果表明，生长诱导的残余应力的明确机制，可以预测在这个框架。
Mixture theory, which can combine continuum theories for the motion and deformation of solids and fluids with general principles of chemistry, is well suited for modeling the complex responses of biological tissues, including tissue growth and remodeling, tissue engineering, mechanobiology of cells and a variety of other active processes. A comprehensive presentation of the equations of reactive mixtures of charged solid and fluid constituents is lacking in the biomechanics literature. This study provides the conservation laws and entropy inequality, as well as interface jump conditions, for reactive mixtures consisting of a constrained solid mixture and multiple fluid constituents. The constituents are intrinsically incompressible and may carry an electrical charge. The interface jump condition on the mass flux of individual constituents is shown to define a surface growth equation, which predicts deposition or removal of material points from the solid matrix, complementing the description of volume growth described by the conservation of mass. A formulation is proposed for the reference configuration of a body whose material point set varies with time. State variables are defined which can account for solid matrix volume growth and remodeling. Constitutive constraints are provided on the stresses and momentum supplies of the various constituents, as well as the interface jump conditions for the electrochemical potential of the fluids. Simplifications appropriate for biological tissues are also proposed, which help reduce the governing equations into a more practical format. It is shown that explicit mechanisms of growth-induced residual stresses can be predicted in this framework.