利用累积环境耦合捕获细胞时空密度的计算框架
Computational framework to capture the spatiotemporal density of cells with a cumulative environmental coupling
摘要：
基于随机代理的模型可以解释数百万个具有时空运动的细胞，这些时空运动可以是不同因素的函数。然而，这些模拟可能在计算上是昂贵的。在这项工作中，我们开发了一种新的计算框架来描述和模拟随机细胞过程，耦合到环境。具体来说，通过放大，我们推导出一个连续的控制方程，认为细胞密度作为时间，空间和累积变量的函数，是耦合到环境条件。对于这个新的控制方程，我们考虑了稳定性，通过能量分析，以及证明唯一性和适定性。为了求解自由空间中的控制方程，我们提出了一种利用基本解的数值方法。作为一个应用程序，我们研究了一个细胞移动在一个无限的域，其中包含一种有毒的化学品，在临界值以上的累积暴露导致细胞死亡。我们说明了这种新的建模框架和相关的数值方法的有效性，通过比较活细胞的密度，从相应的基于代理的模型的结果。
英文摘要：
Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel computational framework to describe and simulate stochastic cellular processes that are coupled to the environment. Specifically, through upscaling, we derive a continuum governing equation that considers the cell density as a function of time, space, and a cumulative variable that is coupled to the environmental conditions. For this new governing equation, we consider the stability through an energy analysis, as well as proving uniqueness and well-posedness. To solve the governing equations in free-space, we propose a numerical method using fundamental solutions. As an application, we study a cell moving in an infinite domain that contains a toxic chemical, where a cumulative exposure above a critical value results in cell death. We illustrate the validity of this new modeling framework and associated numerical methods by comparing the density of live cells to results from the corresponding agent-based model.
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