2019/01/18 by Mark A. J. Chaplain, Chiara Giverso, Chaplain, Mark A. J. +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #35Q92 #35R05 #92C10 #92C17 #Advanced Mathematical Modeling in Engineering #Cellular Mechanics and Interactions #FOS: Biological sciences #Mathematical Biology Tumor Growth #Tissues and Organs (q-bio.TO)
paper · pdf · doi:10.48550/arxiv.1901.10803
openalex publication_date 2019/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a continuum mechanical model of cell invasion through thin\nmembranes. The model consists of a transmission problem for cell volume\nfraction complemented with continuity of stresses and mass flux across the\nsurfaces of the membranes. We reduce the original problem to a limiting\ntransmission problem whereby each thin membrane is replaced by an effective\ninterface, and we develop a formal asymptotic method that enables the\nderivation of a set of biophysically consistent transmission conditions to\nclose the limiting problem. The formal results obtained are validated via\nnumerical simulations showing that the relative error between the solutions to\nthe original transmission problem and the solutions to the limiting problem\nvanishes when the thickness of the membranes tends to zero. In order to show\npotential applications of our effective interface conditions, we employ the\nlimiting transmission problem to model cancer cell invasion through the\nbasement membrane and the metastatic spread of ovarian carcinoma.\n