There is clinical evidence that some people have lived with a benign tumour for their entire life time. This is explained by cancer dormancy which is attributed to the interaction of tumour infiltrating cytotoxic lymphocytes (TICLs) with tumour cells. We present two mathematical models to study the mechanism of interaction of TICLs with tumour cells, with and without clinical intervention. Stability analysis and numerical simulations of the models reveal the existence of a stable tumour dormant state.
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http://dx.doi.org/10.1016/j.mbs.2014.01.002 | DOI Listing |
Math Biosci
March 2014
University of Kwazulu Natal, School of Mathematics, Statistics, and Computer Science, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa. Electronic address:
There is clinical evidence that some people have lived with a benign tumour for their entire life time. This is explained by cancer dormancy which is attributed to the interaction of tumour infiltrating cytotoxic lymphocytes (TICLs) with tumour cells. We present two mathematical models to study the mechanism of interaction of TICLs with tumour cells, with and without clinical intervention.
View Article and Find Full Text PDFOphthalmic Surg Lasers Imaging
March 2012
Gimbel Eye Centre, Calgary, Alberta, Canada.
The authors describe a patient who was found to have bilateral, peripheral iris cysts during preoperative ultrasound biomicroscopy (UBM) assessment prior to toric implantable collamer lens (TICL) implantation. TICL implantation was undertaken with no intraoperative or postoperative complications. The TICLs remained in stable position over a follow-up period of 15 months.
View Article and Find Full Text PDFJ Theor Biol
August 2011
National Institute of Research and Development for Technical Physics, D. Mangeron 47, Iaşi 700050, Romania.
We present a traveling-wave analysis of a reduced mathematical model describing the growth of a solid tumor in the presence of an immune system response in the framework of Scale Relativity theory. Attention is focused upon the attack of tumor cells by tumor-infiltrating cytotoxic lymphocytes (TICLs), in a small multicellular tumor, without necrosis and at some stage prior to (tumor-induced) angiogenesis. For a particular choice of parameters, the underlying system of partial differential equations is able to simulate the well-documented phenomenon of cancer dormancy and propagation of a perturbation in the tumor cell concentration by cnoidal modes, by depicting spatially heterogeneous tumor cell distributions that are characterized by a relatively small total number of tumor cells.
View Article and Find Full Text PDFC R Biol
November 2004
The SIMBIOS Centre, Division of Mathematics, University of Dundee, Dundee, UK.
In this paper we present a travelling-wave analysis of a mathematical model describing the growth of a solid tumour in the presence of an immune system response. From a modelling perspective, attention is focused upon the attack of tumour cells by tumour infiltrating cytotoxic lymphocytes (TICLs), in a small multicellular tumour, without necrosis and at some stage prior to (tumour-induced) angiogenesis. As we have shown in previous work, for a particular choice of parameters, the underlying reaction-diffusion-chemotaxis system of partial differential equations is able to simulate the well-documented phenomenon of cancer dormancy by depicting spatially heterogeneous tumour cell distributions that are characterized by a relatively small total number of tumour cells.
View Article and Find Full Text PDFMath Med Biol
March 2004
The SIMBIOS Centre, Division of Mathematics, University of Dundee, Dundee DD1 4HN, UK.
In this paper a mathematical model describing the growth of a solid tumour in the presence of an immune system response is presented. In particular, attention is focused upon the attack of tumour cells by so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without necrosis and at some stage prior to (tumour-induced) angiogenesis. At this stage the immune cells and the tumour cells are considered to be in a state of dynamic equilibrium--cancer dormancy--a phenomenon which has been observed in primary tumours, micrometastases and residual disease after ablation of the primary tumour.
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