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Register a new userA cellular automata model for avascular solid tumor growth under the effect of therapy
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Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe avascular solid tumor growth, taking into account both the competition between cancer cells and normal cells for nutrients and/or space and a time-dependent proliferation of cancer cells. Gompertzian growth, characteristic of some tumors, is described and some of the features of the time-spatial pattern of solid tumors, such as compact morphology with irregular borders, are captured. The parameter space is studied in order to analyze the occurrence of necrosis and the response to therapy. Our findings suggest that transitions exist between necrotic and non-necrotic phases (no-therapy cases), and between the states of cure and non-cure (therapy cases). To analyze cure, the control and order parameters are, respectively, the highest probability of cancer cell proliferation and the probability of the therapeutic effect on cancer cells. With respect to patterns, it is possible to observe the inner necrotic core and the effect of the therapy destroying the tumor from its outer borders inwards.
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Prediction and control of cancer invasion is a vital problem in medical science. This paper proposes a modern geometric Ricci-flow and entropy based model for control of avascular multicellular tumor spheroid growth and decay. As a tumor growth/decay control tool, a monoclonal antibody therapy is proposed. Keywords: avascular tumor growth and decay, multicellular tumor spheroid, Ricci flow and entropy, nonlinear heat equation, monoclonal antibody cancer therapy
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Demosthenes Ellinas
, Elena P. Papadopoulou
, Yiannis G. Saridakisn (Department of Sciences
2000
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