Journal Article

Inducing catastrophe in malignant growth

Robert A. Gatenby and B. Roy Frieden

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 25, issue 3, pages 267-283
Published in print September 2008 | ISSN: 1477-8599
Published online July 2008 | e-ISSN: 1477-8602 | DOI:
Inducing catastrophe in malignant growth

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  • Applied Mathematics
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Mathematical catastrophe theory is used to describe cancer growth during any time-dependent program a(t) of therapeutic activity. The program may be actively imposed, e.g. as chemotherapy, or occur passively as an immune response. With constant therapy a(t), the theory predicts that cancer mass p(t) grows in time t as a cosine-modulated power law, with power = 1.618···, the Fibonacci constant. The cosine modulation predicts the familiar relapses and remissions of cancer growth. These fairly well agree with clinical data on breast cancer recurrences following mastectomy. Two such studies of 3183 Italian women consistently show an immune system's average activity level of about a = 2.8596 for the women. Fortunately, an optimum time-varying therapy program a(t) is found that effects a gradual approach to full remission over time, i.e. to a chronic disease. Both activity a(t) and cancer mass p(t) monotonically decrease with time, the activity a(t) as 1/(ln t) and mass remission as t94{ – 0.382}. These predicted growth effects have a biological basis in the known presence of multiple alleles during cancer growth.

Keywords: optimal chemotherapy; including catastrophe in malignancy; catastrophe theory; cancer as chronic disease

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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