title: A Multiscale Approach to the Migration of Cancer Stem Cells: Mathematical Modelling and Simulations.
abstract: We propose a multiscale model for the invasion of the extracellular matrix by two types of cancer cells, the differentiated cancer cells and the cancer stem cells. We investigate the epithelial mesenchymal-like transition between them being driven primarily by the epidermal growth factors. We moreover take into account the transdifferentiation program of the cancer stem cells towards the cancer-associated fibroblast cells as well as the fibroblast-driven remodelling of the extracellular matrix. The proposed haptotaxis model combines the macroscopic phenomenon of the invasion of the extracellular matrix by both types of cancer cells with the microscopic dynamics of the epidermal growth factors. We analyse our model in a component-wise manner and compare our findings with the literature. We investigate pathological situations regarding the epidermal growth factors and accordingly propose "mathematical-treatment" scenarios to control the aggressiveness of the tumour.
authors.affiliation: Institute of Mathematics, Johannes Gutenberg-University, Mainz, Germany. sfakiana@uni-mainz.de.
authors.forename: Nikolaos
authors.initials: N
authors.lastname: Sfakianakis
authors.affiliation: Institute of Mathematics, Johannes Gutenberg-University, Mainz, Germany.
authors.forename: Niklas
authors.initials: N
authors.lastname: Kolbe
authors.affiliation: Institute of Molecular Biophysics, Johannes Gutenberg-University, Mainz, Germany.
authors.forename: Nadja
authors.initials: N
authors.lastname: Hellmann
authors.affiliation: Institute of Mathematics, Johannes Gutenberg-University, Mainz, Germany.
authors.forename: Mária
authors.initials: M
authors.lastname: Lukáčová-Medvid'ová
mesh_terms: D002465:Cell Movement; D054338:Cell Transdifferentiation; D003198:Computer Simulation; D058750:Epithelial-Mesenchymal Transition; D005109:Extracellular Matrix / Q000473:pathology / Q000502:physiology; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D014411:Neoplastic Stem Cells / Q000473:pathology / Q000502:physiology*
keywords: Cancer stem cell invasion; Epidermal growth factor receptors; Epithelial mesenchymal transition; Extracellular matrix