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Lattice and continuum modelling of a bioactive porous tissue scaffold.
Mathematical Medicine and Biology ( IF 1.1 ) Pub Date : 2019-09-02 , DOI: 10.1093/imammb/dqy012
Andrew L Krause 1 , Dmitry Beliaev 1 , Robert A Van Gorder 1 , Sarah L Waters 1
Affiliation  

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.

中文翻译:

生物活性多孔组织支架的晶格和连续模型。

生长人造组织的现代方法是将细胞播种到多孔生物材料支架上,并在灌注生物反应器中进行培养,以促进营养物质向生长中细胞的运输。用于组织工程应用的典型细胞生长模型利用空间均匀或空间连续方程式对细胞生长,培养基流量,营养物质运输及其相互作用建模。物理多孔支架的网络结构通常通过现象学或通过诸如数学均化的技术通过这些模型中的参数并入。我们在正方形网格格子上推导一个模型,以证明对多孔支架的网络结构进行显式建模的重要性,并将该模型的结果与文献中改进的连续体模型的结果进行比较。我们通过允许细胞阻塞孔并允许流体的剪切应力影响细胞的生长和死亡来捕获细胞生长与流体流动之间的双向耦合。我们探索了两个模型的参数范围,并证明了每种方法的预测之间在定量和质量上的差异,包括空间模式形成和仅在晶格模型中存在的细胞密度的局部振荡。这些差异表明,对于某些参数方案,对应于特定的细胞类型和支架的几何形状,与典型的连续模型相比,晶格模型在质量上有不同的模型预测。我们的结果为生物活性多孔组织支架的模型选择提供了帮助,有助于成功的组织工程实验和最终在临床上成功的技术的开发。
更新日期:2019-11-01
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