Hollow fibre membrane bioreactors (HFMBs) have been shown to overcome the diffusion limitation of nutrients (e.g., glucose) from the hollow fibres (lumens) to the porous regions of a scaffold (extracapillary space). However, direct monitoring of glucose diffusion inside the HFMBs is almost impossible because of their small size; thus, various computational modelling frameworks have been developed in the past. These models have defined that the glucose diffusivity in the cell culture medium used in the HFMBs was similar to the diffusivity in water. Similarly, other assumptions have been made that do not represent the nutrient transport processes in the HFMB accurately. In addressing these issues, a mathematical model is presented in this paper, where we employ experimentally deduced effective glucose diffusivities of tissue engineering membranes and scaffolds with and without cells along with glucose diffusivity in cell culture medium. The governing equations are non‐dimensionalized, simplified and solved numerically. The results demonstrate the roles of various dimensionless numbers (e.g., Péclet and Damköhler numbers) and non‐dimensional groups of variables on determining the glucose concentration especially in the scaffold region. The result of this study is expected to help optimize designs of HFMB as well as carry out more accurate scaling analyses.

中文翻译：

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中空纤维膜生物反应器中用于生长三维组织的葡萄糖转运的建模

中空纤维膜生物反应器（HFMBs）已显示出克服了营养物质（例如葡萄糖）从中空纤维（内腔）向支架多孔区域（毛细血管外空间）扩散的限制。然而，由于HFMB的体积小，几乎不可能直接监测其扩散。因此，过去已经开发了各种计算建模框架。这些模型定义了，HFMBs中使用的细胞培养基中的葡萄糖扩散率类似于在水中的扩散率。同样，已经做出了其他假设，这些假设不能准确地代表HFMB中的养分传输过程。为了解决这些问题，本文提出了一个数学模型，在这里我们采用实验推导的有组织和无细胞组织工程膜和支架的有效葡萄糖扩散率以及细胞培养基中的葡萄糖扩散率。控制方程是无量纲的，可以简化并通过数值求解。结果证明了各种无因次数（例如佩克雷特和达姆霍勒数）和无因次变量组在确定葡萄糖浓度（尤其是在支架区域）中的作用。预期这项研究的结果将有助于优化HFMB的设计，并进行更准确的比例分析。结果证明了各种无因次数（例如佩克雷特和达姆霍勒数）和无因次变量组在确定葡萄糖浓度（尤其是在支架区域）中的作用。预期这项研究的结果将有助于优化HFMB的设计，并进行更准确的比例分析。结果证明了各种无因次数（例如佩克雷特和达姆霍勒数）和无因次变量组在确定葡萄糖浓度（尤其是在支架区域）中的作用。预期这项研究的结果将有助于优化HFMB的设计，并进行更准确的比例分析。