Lewis Miranda C, Macarthur Ben D, Malda Jos, Pettet Graeme, Please Colin P
School of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, United Kingdom.
Biotechnol Bioeng. 2005 Sep 5;91(5):607-15. doi: 10.1002/bit.20508.
This article investigates heterogeneous proliferation within a seeded three-dimensional scaffold structure with the purpose of improving protocols for engineered tissue growth. A simple mathematical model is developed to examine the very strong interaction between evolving oxygen profiles and cell distributions within cartilaginous constructs. A comparison between predictions based on the model and experimental evidence is given for both spatial and temporal evolution of the oxygen tension and cell number density, showing that behaviour for the first 14 days can be explained well by the mathematical model. The dependency of the cellular proliferation rate on the oxygen tension is examined and shown to be similar in size to previous work but linear in form. The results show that cell-scaffold constructs that rely solely on diffusion for their supply of nutrients will inevitably produce proliferation-dominated regions near the outer edge of the scaffold in situations when the cell number density and oxygen consumption rate exceed a critical level. Possible strategies for reducing such non-uniform proliferation, including the conventional methods of enhancing oxygen transport, are outlined based on the model predictions.
本文研究了接种于三维支架结构内的异质性增殖情况,目的是改进工程组织生长的方案。建立了一个简单的数学模型,以研究软骨构建体内不断变化的氧分布与细胞分布之间非常强烈的相互作用。针对氧张力和细胞数密度的空间和时间演变,给出了基于该模型的预测结果与实验证据之间的比较,结果表明,该数学模型能够很好地解释前14天的行为。研究了细胞增殖速率对氧张力的依赖性,结果表明其大小与先前的工作相似,但形式上呈线性关系。结果表明,在细胞数密度和氧消耗率超过临界水平的情况下,仅依靠扩散来供应营养物质的细胞-支架构建体将不可避免地在支架外边缘附近产生以增殖为主的区域。基于模型预测,概述了减少这种非均匀增殖的可能策略,包括增强氧传输的传统方法。