Unbiased on-lattice domain growth

Abstract

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 in order to incorporate domain growth into on-lattice reaction-diffusion models causes a build up 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 a new method which addresses this unphysical build up of particles at the boundaries, and demonstrate that it is accurate even 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.