Coupling actin dynamics to phase-field in modeling neural growth

In this paper we model the growth of a neural cell together with the actin dynamics taking place at its growing region by constructing a phase-field model. This is done by assigning auxiliary fields to different constituents of the cell in order to differentiate them. Specifically, the inner and outer regions of the neural cell are described by ϕ = 1 and ϕ = 0 respectively, whereas the inside and outside of its leading edge are portrayed by ψ = 1 and ψ = 0. This formulation inherently locates the boundary, which is required to determine the evolution of the underlying actin dynamics. Therefore, it provides an alternative to boundary tracking algorithms. Then the equations governing the molecular workings of the cell specifically those of actin are modified in order to satisfy their corresponding boundary conditions.