The role of porosity and solid matrix compressibility on the mechanical behavior of poroelastic tissues
The role of porosity and solid matrix compressibility on the mechanical behavior of poroelastic tissues
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DOI：
10.1088/2053-1591/aaf5b9
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发表时间：
2019-03-01
影响因子：
2.3
通讯作者：
Merodio, J.
中科院分区：
文献类型：
--
作者：
Dehghani, H.;Penta, R.;Merodio, J.
我们研究了多孔弹性材料的力学和水力特性与流经其孔隙的流体的间隙体积分数(孔隙率)和其弹性(基质)相的可压缩性之间的关系。假设基质的力学行为为线弹性类型，并利用孔洞(孔尺度或微尺度)与平均组织尺寸(宏观尺度)之间的长度尺度分离的渐近均匀化技术进行三维微观结构分析。因此，模型的系数是通过适当的平均值来获得的，该平均值涉及到孔尺度上的周期细胞问题的解。后者采用立方单元中的有限元进行数值求解，假定为十字形的连通圆柱体结构，在宏观尺度上产生三次对称的刚度张量。因此，材料的宏观响应可以用六个参数来完整地表征，即弹性杨氏和剪切模数、泊松比、渗透系数和孔弹性参数，即Biot模数和Biot系数。我们通过改变基质的孔隙率和泊松比进行参数分析，给出了我们的发现。我们的新三维结果是在肿瘤建模的背景下提出的，作为稳健的第一步，以(A)基于其潜在的微观结构来量化多孔弹性材料的宏观响应，(B)将可用于区分良性肿瘤和癌症的组织的可压缩性与其微观结构属性(如孔隙度)相关联，以及(C)揭示Biot模数对基质的孔隙率和可压缩性的重要依赖，这可以为根据可用于传输质量和溶质的流体体积来优化人工结构的设计铺平道路。
We investigate the dependence of the mechanical and hydraulic properties of poroelastic materials on the interstitial volume fraction (porosity) of the fluid flowing through their pores and compressibility of their elastic (matrix) phase. The mechanical behavior of the matrix is assumed of linear elastic type and we conduct a three-dimensional microstructural analysis by means of the asymptotic homogenization technique exploiting the length scale separation between the pores (pore-scale or microscale) and the average tissue size (the macroscale). The coefficients of the model are therefore obtained by suitable averages which involve the solutions of periodic cell problems at the pore-scale. The latter are solved numerically by finite elements in a cubic cell by assuming a cross-shaped interconnected cylindrical structure which results in a cubic symmetric stiffness tensor on the macroscale. Therefore, the macroscale response of the material is fully characterized by six parameters, namely the elastic Young's and shear moduli, Poisson's ratio, the hydraulic conductivity, and the poroelastic parameters, i.e. Biot's modulus and Biot's coefficient. We present our findings in terms of a parametric analysis conducted by varying the porosity as well as the Poisson's ratio of the matrix. Our novel three-dimensional results, which are presented in the context of tumor modeling, serve as a robust first step to (a) quantify the macroscale response of poroelastic materials on the basis of their underlying microstructure, (b) relate the compressibility of the tissue, which can be used to distinguish between benign tumor and cancer, to its microstructural properties (such as porosity), and (c) reveal a nontrivial dependency of Biot's modulus on porosity and compressibility of the matrix, which can pave the way to the optimal design of artificial constructs in terms of fluid volume available for transport of mass and solutes.