Continuum approximations of individual-based models for epithelial monolayers
Continuum approximations of individual-based models for epithelial monolayers
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DOI：
10.1093/imammb/dqp015
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发表时间：
2010-03-01
影响因子：
1.1
通讯作者：
King, J. R.
中科院分区：
文献类型：
--
作者：
Fozard, J. A.;Byrne, H. M.;King, J. R.
这项工作探讨了一个1D的个人为基础的模型（IBM）的系统紧密粘附的细胞，如上皮细胞单层。每个单元占据由其端点的位置限定的有界区域，具有弹性和粘性机械特性，并且经受由粘附到基底产生的阻力。从能量的角度考虑，得到了控制系统演化的微分代数方程。然后，当细胞参数在空间上缓慢变化或在空间上是周期性的（因此可能是异质的，相邻细胞之间有很大的变化）时，在大量细胞N的限制下，用连续模型（偏微分方程系统）来近似IBM。对于具有显著细胞粘度的空间周期性细胞性质，连续模型的平均细胞压力和长度之间的关系被发现是历史依赖的。条款涉及对流衍生物，通常不包括在连续组织模型，确定。通过细胞生长（但不分裂）的细胞聚集体的扩展的具体问题被详细考虑，包括长时间和缓慢的生长速率限制。当相邻细胞的参数在空间中缓慢变化时，连续近似中的O（1/N-2）误差使该方法即使对于适度的N值也能够使用。在空间周期的情况下，被忽略的条款被发现是O（1/N）。该模型还用于检查在伤口愈合测定中观察到的伤口边缘的加速。
This work examines a 1D individual-based model (IBM) for a system of tightly adherent cells, such as an epithelial monolayer. Each cell occupies a bounded region, defined by the location of its endpoints, has both elastic and viscous mechanical properties and is subject to drag generated by adhesion to the substrate. Differential-algebraic equations governing the evolution of the system are obtained from energy considerations. This IBM is then approximated by continuum models (systems of partial differential equations) in the limit of a large number of cells, N, when the cell parameters vary slowly in space or are spatially periodic (and so may be heterogeneous, with substantial variation between adjacent cells). For spatially periodic cell properties with significant cell viscosity, the relationship between the mean cell pressure and length for the continuum model is found to be history dependent. Terms involving convective derivatives, not normally included in continuum tissue models, are identified. The specific problem of the expansion of an aggregate of cells through cell growth (but without division) is considered in detail, including the long-time and slow-growth-rate limits. When the parameters of neighbouring cells vary slowly in space, the O(1/N-2) error in the continuum approximation enables this approach to be used even for modest values of N. In the spatially periodic case, the neglected terms are found to be O(1/N). The model is also used to examine the acceleration of a wound edge observed in wound-healing assays.