In recent years, there has been a move away from the use of static in vitro two-dimensional cell culture models for testing the chemical safety and efficacy of drugs. Such models are increasingly being replaced by more physiologically relevant cell culture systems featuring dynamic flow and/or three-dimensional structures of cells. While it is acknowledged that such systems provide a more realistic environment within which to test drugs, progress is being hindered by a lack of understanding of the physical and chemical environment that the cells are exposed to. Mathematical and computational modelling may be exploited in this regard to unravel the dependency of the cell response on spatio-temporal differences in chemical and mechanical cues, thereby assisting with the understanding and design of these systems. In this paper, we present a mathematical modelling framework that characterizes the fluid flow and solute transport in perfusion bioreactors featuring an inlet and an outlet. To demonstrate the utility of our model, we simulated the fluid dynamics and solute concentration profiles for a variety of different flow rates, inlet solute concentrations and cell types within a specific commercial bioreactor chamber. Our subsequent analysis has elucidated the basic relationship between inlet flow rate and cell surface flow speed, shear stress and solute concentrations, allowing us to derive simple but useful relationships that enable prediction of the behaviour of the system under a variety of experimental conditions, prior to experimentation. We describe how the model may used by experimentalists to define operating parameters for their particular perfusion cell culture systems and highlight some operating conditions that should be avoided. Finally, we critically comment on the limitations of mathematical and computational modelling in this field, and the challenges associated with the adoption of such methods.

中文翻译：

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流体流动和溶质运输的数学模型，用于定义体外灌注细胞培养系统的操作参数。

近年来，人们逐渐不再使用静态体外二维细胞培养模型来测试药物的化学安全性和有效性。此类模型越来越多地被具有细胞动态流动和/或三维结构的生理相关细胞培养系统所取代。尽管人们承认此类系统提供了更真实的药物测试环境，但由于缺乏对细胞所暴露的物理和化学环境的了解，进展受到阻碍。在这方面可以利用数学和计算模型来揭示细胞反应对化学和机械线索时空差异的依赖性，从而有助于理解和设计这些系统。在本文中，我们提出了一个数学建模框架，该框架描述了具有入口和出口的灌注生物反应器中的流体流动和溶质运输。为了证明我们模型的实用性，我们模拟了特定商业生物反应器室内各种不同流速、入口溶质浓度和细胞类型的流体动力学和溶质浓度分布。我们随后的分析阐明了入口流速与细胞表面流速、剪切应力和溶质浓度之间的基本关系，使我们能够得出简单但有用的关系，从而能够在各种实验条件下预测系统的行为。实验。我们描述了实验人员如何使用该模型来定义其特定灌注细胞培养系统的操作参数，并强调一些应避免的操作条件。最后，我们批判性地评论了该领域数学和计算建模的局限性，以及与采用此类方法相关的挑战。