We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

中文翻译：

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离散的连续连续的心脏祖细胞形成和生长的数学模型，为球状簇（心球）。

我们提出了一个离散的连续数学模型，该模型描述了以生物体形式起源的哺乳动物心脏祖细胞的体外生长过程，这些细胞以球体（Cardiospheres）的形式簇生。这种方法是混合的：在细胞水平上是离散的，而在分子水平上是连续的。在本模型中，细胞受自组织集体动力学机制的影响，此外，它们还可以根据随机过程增殖和分化。后两个过程是由环境中存在的化学信号触发和调节的。数值模拟显示了簇状祖细胞的结构和发展，并且与体外实验的结果非常吻合。