Abstract
Cancer-cell invasion is a complex biological process involving cell migration through the extracellular matrix, which is driven by haptotaxis, and the interactions between cancer cells and the surrounding matrix. In this paper, a three-dimensional haptotaxis model that simulates the migration of a cancer cell population, including cell–cell adhesion and cell–matrix adhesion, is proposed. We employ a diffuse interface model that incorporates the mechanism of haptotaxis and the interface energy of cancer cells as well as that between cancer cells and the matrix. The semi-implicit Fourier spectral scheme is applied for high efficiency and numerical stability. The simulations systematically reveal the dynamics of cancer-cell migration and the effect of interface energy on the invasion of cancer cells.
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