Mathematical modeling of cancer cell invasion of tissue: Biological insight from mathematical analysis and computational simulation

Andasari, V; Gerisch, A; Lolas, G; South, AP; Chaplain, MAJ

dc.contributor.author	Andasari, V	en
dc.contributor.author	Gerisch, A	en
dc.contributor.author	Lolas, G	en
dc.contributor.author	South, AP	en
dc.contributor.author	Chaplain, MAJ	en
dc.date.accessioned	2014-03-01T01:35:57Z
dc.date.available	2014-03-01T01:35:57Z
dc.date.issued	2011	en
dc.identifier.issn	0303-6812	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21265
dc.subject	Cancer invasion	en
dc.subject	Haptotaxis	en
dc.subject	Invasion index	en
dc.subject	Organotypic culture	en
dc.subject	Spatio-temporal heterogeneity	en
dc.subject	uPA system	en
dc.subject.classification	Biology	en
dc.subject.classification	Mathematical & Computational Biology	en
dc.subject.other	urokinase	en
dc.subject.other	article	en
dc.subject.other	biological model	en
dc.subject.other	cancer invasion	en
dc.subject.other	computer simulation	en
dc.subject.other	extracellular matrix	en
dc.subject.other	human	en
dc.subject.other	metabolism	en
dc.subject.other	pathology	en
dc.subject.other	physiology	en
dc.subject.other	Computer Simulation	en
dc.subject.other	Extracellular Matrix	en
dc.subject.other	Humans	en
dc.subject.other	Models, Biological	en
dc.subject.other	Neoplasm Invasiveness	en
dc.subject.other	Urokinase-Type Plasminogen Activator	en
dc.title	Mathematical modeling of cancer cell invasion of tissue: Biological insight from mathematical analysis and computational simulation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00285-010-0369-1	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00285-010-0369-1	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model. © 2010 Springer-Verlag.	en
heal.publisher	SPRINGER	en
heal.journalName	Journal of Mathematical Biology	en
dc.identifier.doi	10.1007/s00285-010-0369-1	en
dc.identifier.isi	ISI:000291604600007	en
dc.identifier.volume	63	en
dc.identifier.issue	1	en
dc.identifier.spage	141	en
dc.identifier.epage	171	en