Phase-field modeling for curvature-dependent tissue growth on surfaces

We propose a novel phase-field model for simulating curvature-dependent and surface-limited tissue growth on curved surfaces. The proposed mathematical model consists of a modified Allen–Cahn (AC) equation with a non-standard variable mobility and a growth term that depends on curvature and surface limitations. To solve the equations numerically, we use an operator splitting technique. We split the governing equation into a modified AC equation, and curvature-dependent and surface limited growth equation. To validate the high performance of the proposed mathematical model in realistic simulations, we conduct several numerical simulations such as those with synthetic conditions and comparisons with real experimental data. The computational results demonstrate the robustness and efficiency of the new phase-field model in accurately capturing realistic tissue growth phenomena on curved surfaces.