Mathematical modelling, analysis and numerical simulations for the influence of heat shock proteins on tumour invasion
Guelnihal Meral, Christina Surulescu
article (Uluslararası, Hakemli) | Yazar(lar): Guelnihal Meral, Christina Surulescu | Yıl: 2013 | Dergi/Kurum: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | İndeks: WOS.SCI | DOI: 10.1016/j.jmaa.2013.06.017 | Anahtar Kelimeler: Tumour invasion, Heat shock proteins, Multiscale model, Time delay, Reaction-diffusion
Invasion is a key property of tumour cells for building metastasis. A class of functionally related proteins called heat shock proteins (HSPs), the expression of which is increased when cells are exposed to elevated temperatures or other stress, play an important role in the invasion. In this paper we develop a mathematical model focusing on the effect of HSPs on the tumour cell migration. The resulting multiscale setting accounts both for the microscopic, intracellular level on which these proteins are acting and for the macroscopic level of the cell population. We prove the local existence of a unique positive solution and perform numerical simulations in order to illustrate the behaviour of cancer cells w.r.t. the fibre density of the tissue and the matrix degrading enzymes, along with the effect of HSPs. (C) 2013 Elsevier Inc. All rights reserved.