论文标题
机械力的自适应时间整合在基于中心的生物细胞群体模型中
Adaptive time integration of mechanical forces in center-based models for biological cell populations
论文作者
论文摘要
基于中心的模型用于模拟胚胎发育或癌症生长过程中生物细胞的机械行为。为了允许模拟从几个单个细胞到数千个或更多的生物群体，这些模型必须在数值上有效，同时在单个细胞轨迹的水平上相当准确。在这项工作中，我们通过在数值方法中自适应选择时间步骤来提高基于中心模型的仿真的鲁棒性，准确性和效率。我们根据数值错误的局部估计值和该方法的稳定性，在使用显式前向Euler方法的情况下，我们研究了向前和向后Euler方法的单率时间步进的增益。此外，我们提出了一个多阶段时间步进方案，该方案模拟具有较高的局部力梯度（例如，在细胞分裂之后发生）的区域，该区域在较大的单个时间步长中，用于具有更顺畅力量的区域。比较数值实验中不同模型系统的这些方法。我们得出的结论是，自适应单率向前的Euler方法在减少壁时钟时间的模拟方面会带来显着增长，同时消除了手动确定合适的时间步长的需求。
Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to many thousands or more, these models have to be numerically efficient, while being reasonably accurate on the level of individual cell trajectories. In this work, we increase the robustness, accuracy, and efficiency of the simulation of center-based models by choosing the time steps adaptively in the numerical method. We investigate the gain in using single rate time stepping for the forward and backward Euler methods, based on local estimates of the numerical errors and the stability of the method in the case of the explicit forward Euler method. Furthermore, we propose a multirate time stepping scheme that simulates regions with high local force gradients (e.g. as they happen after cell division) with multiple smaller time steps within a larger single time step for regions with smoother forces. These methods are compared for different model systems in numerical experiments. We conclude that the adaptive single rate forward Euler method results in significant gains in terms of reduced wall clock times for the simulation of a linearly growing tissue, while at the same time eliminating the need for manual determination of a suitable time step size.
