Biphasic behaviour in malignant invasion

Mathematical Medicine and Biology : a Journal of the IMA
Ben P MarchantHelen M Byrne

Abstract

Invasion is an important facet of malignant growth that enables tumour cells to colonise adjacent regions of normal tissue. Factors known to influence such invasion include the rate at which the tumour cells produce tissue-degrading molecules, or proteases, and the composition of the surrounding tissue matrix. A common feature of experimental studies is the biphasic dependence of the speed at which the tumour cells invade on properties such as protease production rates and the density of the normal tissue. For example, tumour cells may invade dense tissues at the same speed as they invade less dense tissue, with maximal invasion seen for intermediate tissue densities. In this paper, a theoretical model of malignant invasion is developed. The model consists of two coupled partial differential equations describing the behaviour of the tumour cells and the surrounding normal tissue. Numerical methods show that the model exhibits steady travelling wave solutions that are stable and may be smooth or discontinuous. Attention focuses on the more biologically relevant, discontinuous solutions which are characterised by a jump in the tumour cell concentration. The model also reproduces the biphasic dependence of the tumour cell invasion...Continue Reading

Citations

Mar 26, 2011·Journal of Mathematical Biology·Anita Häcker
Jun 28, 2011·Annals of Biomedical Engineering·Saheli SarkarHarihara Baskaran
Aug 25, 2012·Computational and Mathematical Methods in Medicine·Fatemeh Leyla MoghaddasiLoredana Marcu
Jan 24, 2016·Journal of Theoretical Biology·Lotte SewaltSanjeeva Balasuriya
May 15, 2013·Mathematical Biosciences·Matthew J SimpsonScott W McCue
Sep 3, 2010·Nonlinearity·J S LowengrubV Cristini
Nov 18, 2018·Bulletin of Mathematical Biology·Alexander P BrowningMatthew J Simpson

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