In this paper, we revisit our previous work in which we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. The underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearization of the underlying multiphase model (whose nonlinearity poses a significant challenge for such analyses), we obtain, by means of multiple-scale homogenization, a simplified macroscale model that nevertheless retains explicit dependence on both the microscale scaffold structure and the tissue dynamics, via so-called unit-cell problems that provide permeability tensors to parameterize the macroscale description. In our previous work, the cell problems retain macroscale dependence, posing significant challenges for computational implementation of the eventual macroscopic model; here, we obtain a decoupled system whereby the quasi-steady cell problems may be solved separately from the macroscale description. Moreover, we indicate how the formulation is influenced by a set of alternative microscale boundary conditions.

中文翻译：

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营养受限组织生长的多相多尺度模型，第 II 部分：简化描述

在本文中，我们重新审视了我们之前的工作，其中我们得出了一个有效的宏观描述，适用于描述多孔组织工程支架内生物组织的生长。潜在的组织动力学被描述为多相混合物，从而自然地适应诸如间质生长和活跃细胞运动等特征。通过基础多相模型的线性化（其非线性对此类分析构成重大挑战），我们通过多尺度均质化获得了一个简化的宏观模型，该模型仍然保留了对微尺度支架结构和组织动力学的明确依赖性，通过所谓的晶胞问题提供渗透性张量来参数化宏观尺度描述。在我们之前的工作中，细胞问题保留了宏观尺度依赖性，对最终宏观模型的计算实现提出了重大挑战；在这里，我们获得了一个解耦系统，准稳态单元问题可以与宏观描述分开解决。此外，我们指出了公式如何受到一组替代微尺度边界条件的影响。