Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells, it is theoretically and numerically advantageous to replace spatial extended cells with point sources, in particular when cell numbers are large, but still so small that a continuum density description cannot be justified, or when cells are moving. We show that inhomogeneous flux density over the cell boundary may be realized in a point source approach, thus maintaining computational efficiency, by utilizing multiple, clustered point sources (and sinks). In this report, we limit ourselves to a sinusoidal function as flux density in the spatial exclusion model, and we show how to determine the amplitudes of the Dirac delta points in the point source model, such that the deviation between the point source model and the spatial exclusion model is small.

翻译：生物细胞能够向直接环境中释放化合物，这些化合物通常在其细胞膜上呈非均匀分布，随后通过扩散传播。在对这类细胞群体进行数学建模与仿真时，理论上和数值上采用点源替代空间扩展的细胞具有显著优势，尤其当细胞数量较大但仍不足以采用连续密度描述，或细胞处于运动状态时。我们证明，通过使用多个聚集的点源（及汇），可以在点源方法中实现细胞边界上的非均匀通量密度，从而保持计算效率。在本报告中，我们限定空间排斥模型中的通量密度为正弦函数，并展示了如何确定点源模型中狄拉克δ点的幅值，以使点源模型与空间排斥模型之间的偏差最小化。