Predoi-Racila M, Stroe M C, Crolet J M
Department of Applied Mathematics, University of Craiova, Craiova, Romania.
Comput Methods Biomech Biomed Engin. 2010 Feb;13(1):81-9. doi: 10.1080/10255842.2010.493732.
Cortical bone is more and more considered as a porous medium and this induces the necessity of the determination of the physical properties associated with such a concept: the porosity and the permeability. If porosity does not present a major problem, at least for the order of magnitude, there is a difficulty for the permeability. According to experimental sources, values vary between 10(- 13) and 10(- 23) m(2): it seems obvious that the same entities have not been measured. This article proposes a new vision of the permeability based on a concept of multi-scale medium corresponding to the scales already introduced in the SiNuPrOs model which has been developed for cortical bone. According to this model, several architectural levels are proposed and a mathematical development based on the homogenisation theory, which can be applied to each of these levels, allows a numerical computation of the permeability tensor coefficients. A comparative analysis of our simulations and some experimental results (already published) shows a good accordance with the literature.
皮质骨越来越被视为一种多孔介质，这就使得确定与该概念相关的物理性质成为必要：孔隙率和渗透率。如果孔隙率至少在数量级上不存在重大问题，那么渗透率则存在困难。根据实验数据，其值在10^(-13) 到10^(-23) 平方米之间变化：显然测量的并非相同的实体。本文基于与为皮质骨开发的SiNuPrOs模型中已引入的尺度相对应的多尺度介质概念，提出了一种关于渗透率的新观点。根据该模型，提出了几个结构层次，并且基于均匀化理论的数学推导（可应用于这些层次中的每一个）能够对渗透率张量系数进行数值计算。对我们的模拟结果与一些已发表的实验结果进行的对比分析表明，与文献结果吻合良好。
