多细胞组织离子输运的均匀化理论
Homogenization Theory of Ion Transportation in Multicellular Tissue
摘要：
生物组织中的离子输运在许多生物学和病理学问题的研究中是至关重要的。一些多细胞结构，如血管壁上的平滑肌，可以被视为周期性的双域结构，其由细胞内空间和细胞外空间以及介于两者之间的半透膜组成。借助双尺度均匀化理论，在考虑非线性交界条件的电中性（EN）微尺度模型的基础上，将膜看作电容器和电阻器的组合，建立了宏观模型.细胞内空间的连通性也被考虑在内。如果胞内空间是完全连通的，并形成一个合胞体，则宏观模型是一个双主非线性耦合偏微分方程系统。否则，当细胞内的细胞是不连接的，宏观尺度模型的细胞内空间是一个普通的微分系统与源/汇项从连接的细胞外空间。
英文摘要：
Ion transport in biological tissues is crucial in the study of many biological and pathological problems. Some multi-cellular structures, like smooth muscles on the vessel walls, could be treated as periodic bi-domain structures, which consist of intracellular space and extracellular space with semipermeable membranes in between. With the aid of two-scale homogenization theory, macro-scale models are proposed based on an electro-neutral (EN) microscale model with nonlinear interface conditions, where membranes are treated as combinations of capacitors and resistors. The connectivity of intracellular space is also taken into consideration. If the intracellular space is fully connected and forms a syncytium, then the macroscale model is a bidomain nonlinear coupled partial differential equations system. Otherwise, when the intracellular cells are not connected, the macroscale model for intracellular space is an ordinary differential system with source/sink terms from the connected extracellular space.
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