BACKGROUND Many biological soft tissues are hydrated porous hyperelastic materials, which consist of a complex solid skeleton with fine voids and fluid filling these voids. Mechanical interactions between the solid and the fluid in hydrated porous tissues have been analyzed by finite element methods (FEMs) in which the mixture theory was introduced in various ways. Although most of the tissues are surrounded by deformable membranes that control transmembrane flows, the boundaries of the tissues have been treated as rigid and/or freely permeable in these studies. The purpose of this study was to develop a method for the analysis of hydrated porous hyperelastic tissues surrounded by deformable membranes that control transmembrane flows. RESULTS For this, we developed a new nonlinear finite element formulation of the mixture theory, where the nodal unknowns were the pore water pressure and solid displacement. This method allows the control of the fluid flow rate across the membrane using Neumann boundary condition. Using the method, we conducted a compression test of the hydrated porous hyperelastic tissue, which was surrounded by a flaccid impermeable membrane, and a part of the top surface of this tissue was pushed by a platen. The simulation results showed a stress relaxation phenomenon, resulting from the interaction between the elastic deformation of the tissue, pore water pressure gradient, and the movement of fluid. The results also showed that the fluid trapped by the impermeable membrane led to the swelling of the tissue around the platen. CONCLUSIONS These facts suggest that our new method can be effectively used for the analysis of a large deformation of hydrated porous hyperelastic material surrounded by a deformable membrane that controls transmembrane flow, and further investigations may allow more realistic analyses of the biological soft tissues, such as brain edema, brain trauma, the flow of blood and lymph in capillaries and pitting edema.

中文翻译：

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对可控跨膜流动的可变形膜包围的生物软组织的有限元分析。

背景技术许多生物软组织是水合的多孔超弹性材料，其由具有细小空隙的复杂固体骨架和填充这些空隙的流体组成。通过有限元方法（FEM）分析了水合多孔组织中固体与流体之间的机械相互作用，其中以多种方式引入了混合理论。尽管大多数组织被控制跨膜流动的可变形膜围绕，但在这些研究中，组织的边界已被视为刚性和/或自由渗透的。这项研究的目的是开发一种分析可变形膜包围的水化多孔超弹性组织的方法，该可变形膜控制着跨膜的流动。结果为此，我们开发了一种新的混合理论非线性有限元公式，节点未知数是孔隙水压力和固体位移。该方法允许使用诺伊曼边界条件控制穿过膜的流体流速。使用该方法，我们对水合的多孔超弹性组织进行了压缩测试，该组织被松弛的不透性膜包围，并且该组织的顶表面的一部分被压板推动。仿真结果表明，应力松弛现象是由组织的弹性变形，孔隙水压力梯度和流体运动之间的相互作用引起的。结果还表明，不可渗透膜捕获的流体导致压板周围的组织肿胀。