Conference Paper

Cancer disease: integrative modelling approaches

Sch. of Math. Sci., Nottingham Univ.
DOI: 10.1109/ISBI.2006.1625040 Conference: Biomedical Imaging: Nano to Macro, 2006. 3rd IEEE International Symposium on
Source: DBLP


Cancer is a complex disease in which a variety of phenomena interact over a wide range of spatial and temporal scales. In this article a theoretical framework will be introduced that is capable of linking together such processes to produce a detailed model of vascular tumour growth. The model is formulated as a hybrid cellular automaton and contains submodels that describe subcellular, cellular and tissue level features. Model simulations will be presented to illustrate the effect that coupling between these different elements has on the tumour's evolution and its response to chemotherapy

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    ABSTRACT: The mathematical analysis of the tumour growth attracted a lot of interest in the last two decades. However, as of today no generally accepted model for tumour growth exists. This is due partially to the incomplete understanding of the related pathology as well as the extremely complicated procedure that guides the evolution of a tumour. In the present work, we analyse the stability of a spherical tumour for four continuous models of an avascular tumour. Conditions for the stability are stated and the results are implemented numerically. It is observed that the steady-state radii that secure the stability of the tumour are different for each of the four models, although the differences are not very pronounced. © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
    Mathematical Medicine and Biology 05/2015; DOI:10.1093/imammb/dqv016 · 1.66 Impact Factor