Resonance and anti-resonance in the design of chemotherapeutic protocols.
Agur, Z. (1998)
Journal of Theoretical Medicine
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Agur, Z. (1998)
Journal of Theoretical Medicine
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A. Q. Cai, Y. Peng, J. Wells, X. Dai, Q. Nie (2009)
Mathematical Modelling of Natural Phenomena
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The maintenance of a stable stem cell population in the epidermis is important for robust regeneration of the stratified epithelium. The population size is usually regulated by cell secreted extracellular signalling molecules as well as intracellular molecules. In this paper, a simple model incorporating both levels of regulation is developed to examine the balance between growth and differentiation for the stem cell population. In particular, the dynamics of a known differentiation regulator...
Solyanik, Galina I., Serikov, Alexander A. (2000)
Journal of Theoretical Medicine
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Arino, O., Sánchez, E. (1997)
Journal of Theoretical Medicine
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G. Kapitanov (2012)
Mathematical Modelling of Natural Phenomena
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There is evidence that cancer develops when cells acquire a sequence of mutations that alter normal cell characteristics. This sequence determines a hierarchy among the cells, based on how many more mutations they need to accumulate in order to become cancerous. When cells divide, they exhibit telomere loss and differentiate, which defines another cell hierarchy, on top of which is the stem cell. We propose a mutation-generation model, ...
Claude Basdevant, Jean Clairambault, Francis Lévi (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control...