标题： 分化细胞行为：一种使用测度论的多尺度方法 显示英文标题

标题： Differentiated cell behavior: a multiscale approach using measure theory

摘要： 本文讨论了从基础物理粒子系统的个体描述中推导出细胞种群的集体模型。 通过考虑细胞的空间分布作为随时间变化的测度，而不是个别细胞的路径，我们得到了源于单个组分细胞表观行为的系综表示。 特别是，作为我们方法的一个关键优势，系统的表示尺度，即微观/离散与宏观/连续，可以根据上述测度所给定的空间结构事后选择。 本文特别关注基于细胞特定功能的不同尺度的应用。 考虑了一个两群体混合系统，其中具有专门/分化表型的细胞被当作离散的质点群体处理，而未专门/未分化细胞团则用连续近似表示。 数值模拟和分析研究强调了一些生物相关参数在决定这种混合细胞系统特定演化中的作用。 显示英文摘要

摘要： This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving measures, rather than at individual cell paths, we obtain an ensemble representation stemming from the phenomenological behavior of the single component cells. In particular, as a key advantage of our approach, the scale of representation of the system, i.e., microscopic/discrete vs. macroscopic/continuous, can be chosen a posteriori according only to the spatial structure given to the aforesaid measures. The paper focuses in particular on the use of different scales based on the specific functions performed by cells. A two-population hybrid system is considered, where cells with a specialized/differentiated phenotype are treated as a discrete population of point masses while unspecialized/undifferentiated cell aggregates are represented with a continuous approximation. Numerical simulations and analytical investigations emphasize the role of some biologically relevant parameters in determining the specific evolution of such a hybrid cell system.