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Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models
Bulletin of Mathematical Biology ( IF 3.5 ) Pub Date : 2020-10-01 , DOI: 10.1007/s11538-020-00810-2
Sonja Mathias 1 , Adrien Coulier 1 , Anass Bouchnita 1, 2 , Andreas Hellander 1
Affiliation  

Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.

中文翻译:

力函数公式对基于中心的模型数值模拟的影响

基于中心或细胞中心的模型是多细胞系统计算研究的框架,广泛用于癌症建模和计算发育生物学。这些模型的核心是用于更新细胞位置的数值方法和编码细胞成对机械相互作用的力函数。对于后者,有多种选择可能会影响所捕获的生物行为以及模拟的稳健性和效率。例如,基于中心的模型的可用开源软件实现依赖于不同的力函数来实现其默认行为,并且建模者要知道它们是否可以互换并不容易。我们的研究解决了这个问题,并有助于从数值角度理解三种流行的力函数的潜力和局限性。我们凭经验表明,选择力参数使得细胞分裂后两个细胞的弛豫时间在不同力函数之间保持一致,导致在强烈细胞增殖后机械弛豫的二维单层的种群半径具有良好的一致性。此外,我们报告说数值稳定性不足以防止细胞分裂后的非物理细胞轨迹,因此,太大的时间步长会导致种群水平的几何差异。我们凭经验表明,选择力参数使得细胞分裂后两个细胞的弛豫时间在不同力函数之间保持一致,导致在强烈细胞增殖后机械弛豫的二维单层的种群半径具有良好的一致性。此外,我们报告说数值稳定性不足以防止细胞分裂后的非物理细胞轨迹,因此,太大的时间步长会导致种群水平的几何差异。我们凭经验表明,选择力参数使得细胞分裂后两个细胞的弛豫时间在不同力函数之间保持一致,导致在强烈细胞增殖后机械弛豫的二维单层的种群半径具有良好的一致性。此外,我们报告说数值稳定性不足以防止细胞分裂后的非物理细胞轨迹,因此,太大的时间步长会导致种群水平的几何差异。
更新日期:2020-10-01
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