**Mathematical modeling of cancer cell invasion of tissue : biological insight from mathematical analysis and computational simulation.** / Andasari, Vivi; Gerisch, Alf; Lolas, Georgios; South, Andrew P.; Chaplain, Mark A. J.

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Andasari, V, Gerisch, A, Lolas, G, South, AP & Chaplain, MAJ 2011, 'Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation' *Journal of Mathematical Biology*, vol 63, no. 1, pp. 141-171. DOI: 10.1007/s00285-010-0369-1

Andasari, V., Gerisch, A., Lolas, G., South, A. P., & Chaplain, M. A. J. (2011). Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation. *Journal of Mathematical Biology*, *63*(1), 141-171. DOI: 10.1007/s00285-010-0369-1

Andasari V, Gerisch A, Lolas G, South AP, Chaplain MAJ. Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation. Journal of Mathematical Biology. 2011 Jul;63(1):141-171. Available from, DOI: 10.1007/s00285-010-0369-1

@article{f370b1b3bca446a7b14e7e1de638633d,

title = "Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation",

keywords = "Cancer invasion, uPA system, Haptotaxis, Spatio-temporal heterogeneity, Organotypic culture, Invasion index, PLASMINOGEN ACTIVATION SYSTEM, EXTRACELLULAR-MATRIX, TUMOR-GROWTH, SOLID TUMOR, CHEMOTAXIS, ADHESION, HETEROGENEITY, ANGIOGENESIS, METASTASIS, MICROENVIRONMENT",

author = "Vivi Andasari and Alf Gerisch and Georgios Lolas and South, {Andrew P.} and Chaplain, {Mark A. J.}",

year = "2011",

month = "7",

doi = "10.1007/s00285-010-0369-1",

volume = "63",

pages = "141--171",

journal = "Journal of Mathematical Biology",

issn = "0303-6812",

publisher = "Springer Verlag",

number = "1",

}

TY - JOUR

T1 - Mathematical modeling of cancer cell invasion of tissue

T2 - Journal of Mathematical Biology

AU - Andasari,Vivi

AU - Gerisch,Alf

AU - Lolas,Georgios

AU - South,Andrew P.

AU - Chaplain,Mark A. J.

PY - 2011/7

Y1 - 2011/7

N2 - 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.

AB - 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.

KW - Cancer invasion

KW - uPA system

KW - Haptotaxis

KW - Spatio-temporal heterogeneity

KW - Organotypic culture

KW - Invasion index

KW - PLASMINOGEN ACTIVATION SYSTEM

KW - EXTRACELLULAR-MATRIX

KW - TUMOR-GROWTH

KW - SOLID TUMOR

KW - CHEMOTAXIS

KW - ADHESION

KW - HETEROGENEITY

KW - ANGIOGENESIS

KW - METASTASIS

KW - MICROENVIRONMENT

U2 - 10.1007/s00285-010-0369-1

DO - 10.1007/s00285-010-0369-1

M3 - Article

VL - 63

SP - 141

EP - 171

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 1

ER -