Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom.
Probability Laboratory, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom.
Phys Rev E. 2019 Dec;100(6-1):063307. doi: 10.1103/PhysRevE.100.063307.
Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and proliferation are of great importance. A previously well-used method to incorporate domain growth into on-lattice reaction-diffusion models causes a buildup of particles on the boundaries of the domain, which is particularly evident when diffusion is low in comparison to the rate of domain growth. Here we present an alternative method which addresses this unphysical buildup of particles at the boundaries and demonstrate that it is accurate for scenarios in which the previous method fails. Further, we discuss for which parameter regimes it is feasible to continue using the original method due to diffusion dominating the domain growth mechanism.
领域增长是生物学许多领域的关键过程，包括胚胎发育、组织生长和肢体再生。因此，将其纳入细胞运动、相互作用和增殖的传统模型中的机制非常重要。一种以前常用的将领域增长纳入晶格反应扩散模型的方法会导致颗粒在领域边界处积聚，当扩散与领域增长速率相比较低时，这种积聚尤其明显。在这里，我们提出了一种替代方法来解决边界处颗粒的这种非物理积聚，并证明在以前的方法失败的情况下它是准确的。此外，我们还讨论了由于扩散主导领域增长机制，在哪些参数范围内继续使用原始方法是可行的。
