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Central Upwind Scheme for Solving Multivariate Cell Population Balance Models

机译：解决多元细胞种群平衡模型的中央迎风方案

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摘要

Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Because of the included level of details, multi-variable cell population balance models (PBMs) offer the most general way to describe the complicated phenomena associated with cell growth, substrate consumption and product formation. For that reason, solving and understanding of such models are essential to predict and control cell growth in the processes of biotechnological interest. Such models typically consist of a partial integro-differential equation for describing cell growth and an ordinary integro-differential equation for representing substrate consumption. However, the involved mathematical complexities make their numerical solutions challenging for the given numerical scheme. In this article, the central upwind scheme is applied to solve the single-variate and bivariate cell population balance models considering equal and unequal partitioning of cellular materials. The validity of the developed algorithms is verified through several case studies. It was found that the suggested scheme is more reliable and effective.
机译：微生物培养物由异质细胞组成，异质细胞的大小和细胞内DNA，蛋白质和其他成分的浓度不同。由于所包含的详细程度，多变量细胞种群平衡模型（PBM）提供了描述细胞生长，底物消耗和产物形成相关的复杂现象的最通用方法。因此，解决和理解此类模型对于预测和控制生物技术感兴趣过程中的细胞生长至关重要。此类模型通常由用于描述细胞生长的部分积分微分方程和用于表示底物消耗的普通积分微分方程组成。但是，所涉及的数学复杂性使其数值解对于给定的数值方案而言具有挑战性。在本文中，考虑到细胞材料分配的相等和不相等，采用中央迎风方案来求解单变量和双变量细胞群体平衡模型。通过几个案例研究验证了所开发算法的有效性。发现所提出的方案是更可靠和有效的。

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