Spatio-temporal dynamics of the immune system response to cancer

Mark Chaplain; Vladimir A. Kuznetsov; Z. H. James; L. A. Stepanova

Spatio-temporal dynamics of the immune system response to cancer

Mark Chaplain
, Vladimir A. Kuznetsov
, Z. H. James
, L. A. Stepanova

Research output: Contribution to conference › Paper

Abstract

In this paper, a mathematical model describing the one-dimensional growth of a solid tumour (for example, a malignant melanoma of the skin) in the presence of an immune system response, is-presented. In particular, attention is focussed upon the interaction of tumour cells with so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without central necrosis and at some stage prior to angiogenesis. At this stage the immune cells and the tumour cells are in a state of dynamic equilibrium (cancer dormancy). The resulting system of three nonlinear partial differential equations is analysed and numerical simulations are presented. The numerical simulations demonstrate the existence of cell distributions that are quasi-stationary in time but unstable and heterogeneous in space. The resulting rich spatio-temporal dynamic behaviour of the system is compared with actual experimental evidence.

Original language	English
Publication status	Published - 1997
Event	International Conference on Mathematical Models in Medical and Health Sciences - Nashville, United States Duration: 28 May 1997 → 31 May 1997

Conference

Conference	International Conference on Mathematical Models in Medical and Health Sciences
Country/Territory	United States
City	Nashville
Period	28/05/97 → 31/05/97

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Tumour necrosis factor
T cell recognition
Mathematical models

Spatio-temporal dynamics of the immune system response to cancer
Chaplain, M., Kuznetsov, V. A., James, Z. H., Davidson, F. & Stepanova, L. A., 1998, Mathematical models in medical and health science. Mary Ann, H., Gieri, S. & Glenn F., W. (eds.). Vanderbilt University Press
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Cite this

@conference{202286e3dc9c47a0bc2211d37b5d7906,

title = "Spatio-temporal dynamics of the immune system response to cancer",

abstract = "In this paper, a mathematical model describing the one-dimensional growth of a solid tumour (for example, a malignant melanoma of the skin) in the presence of an immune system response, is-presented. In particular, attention is focussed upon the interaction of tumour cells with so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without central necrosis and at some stage prior to angiogenesis. At this stage the immune cells and the tumour cells are in a state of dynamic equilibrium (cancer dormancy). The resulting system of three nonlinear partial differential equations is analysed and numerical simulations are presented. The numerical simulations demonstrate the existence of cell distributions that are quasi-stationary in time but unstable and heterogeneous in space. The resulting rich spatio-temporal dynamic behaviour of the system is compared with actual experimental evidence.",

keywords = "Tumour necrosis factor, T cell recognition, Mathematical models",

author = "Mark Chaplain and Kuznetsov, \{Vladimir A.\} and James, \{Z. H.\} and Stepanova, \{L. A.\}",

year = "1997",

language = "English",

note = "International Conference on Mathematical Models in Medical and Health Sciences ; Conference date: 28-05-1997 Through 31-05-1997",

}

TY - CONF

T1 - Spatio-temporal dynamics of the immune system response to cancer

AU - Chaplain, Mark

AU - Kuznetsov, Vladimir A.

AU - James, Z. H.

AU - Stepanova, L. A.

PY - 1997

Y1 - 1997

N2 - In this paper, a mathematical model describing the one-dimensional growth of a solid tumour (for example, a malignant melanoma of the skin) in the presence of an immune system response, is-presented. In particular, attention is focussed upon the interaction of tumour cells with so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without central necrosis and at some stage prior to angiogenesis. At this stage the immune cells and the tumour cells are in a state of dynamic equilibrium (cancer dormancy). The resulting system of three nonlinear partial differential equations is analysed and numerical simulations are presented. The numerical simulations demonstrate the existence of cell distributions that are quasi-stationary in time but unstable and heterogeneous in space. The resulting rich spatio-temporal dynamic behaviour of the system is compared with actual experimental evidence.

AB - In this paper, a mathematical model describing the one-dimensional growth of a solid tumour (for example, a malignant melanoma of the skin) in the presence of an immune system response, is-presented. In particular, attention is focussed upon the interaction of tumour cells with so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without central necrosis and at some stage prior to angiogenesis. At this stage the immune cells and the tumour cells are in a state of dynamic equilibrium (cancer dormancy). The resulting system of three nonlinear partial differential equations is analysed and numerical simulations are presented. The numerical simulations demonstrate the existence of cell distributions that are quasi-stationary in time but unstable and heterogeneous in space. The resulting rich spatio-temporal dynamic behaviour of the system is compared with actual experimental evidence.

KW - Tumour necrosis factor

KW - T cell recognition

KW - Mathematical models

M3 - Paper

T2 - International Conference on Mathematical Models in Medical and Health Sciences

Y2 - 28 May 1997 through 31 May 1997

ER -

Spatio-temporal dynamics of the immune system response to cancer

Abstract

Conference

UN SDGs

Keywords

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Research output

Spatio-temporal dynamics of the immune system response to cancer

Cite this