Gradient method for finding optimal scheduling in infinite dimensional models of chemotherapy.
Smieja, Jaroslaw, Swierniak, Andrzej, Duda, Zdzislaw (2000)
Journal of Theoretical Medicine
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Smieja, Jaroslaw, Swierniak, Andrzej, Duda, Zdzislaw (2000)
Journal of Theoretical Medicine
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Andrzej Świerniak, Urszula Ledzewicz, Heinz Schättler (2003)
International Journal of Applied Mathematics and Computer Science
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We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models...
Fister, K. Renee, Lenhart, Suzanne, McNally, Joseph Scott (1998)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Zarei, H., Kamyad, A.V., Farahi, M.H. (2011)
Computational & Mathematical Methods in Medicine
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Dawson, A., Hillen, T. (2006)
Computational & Mathematical Methods in Medicine
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de Pillis, L.G., Radunskaya, A. (2001)
Journal of Theoretical Medicine
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Brazzoli, I., Chauviere, A. (2006)
Computational & Mathematical Methods in Medicine
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Hedican, Erin B., Kemper, John T., Lanie, Nicole M. (2007)
Computational & Mathematical Methods in Medicine
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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...
Gumel, A.B., Zhang, Xuewu, Shivakumar, P.N., Garba, M.L., Sahai, B.M. (2002)
Journal of Theoretical Medicine
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Duffin, R.Paul, Tullis, Richard H. (2002)
Journal of Theoretical Medicine
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