Optimal strategy in chemotherapy for a Gompertzian model of cancer growth

• Autorzy: Maroński R.
• Języki publikacji: EN

Abstrakty

EN

The problem of optimal cancer chemotherapy is reconsidered. For the assumed result of the therapy the cumulative negative toxic effect of the drug is minimized. The unknown function to be optimized is the time-dependent dose of the drug. The Gompertzian model of cell population growth is employed. The formulated problem of the calculus of variations is solved using the method of Miele (the method of extremization of linear integrals via Green’s theorem). The optimal solution is unique and of “bang-bang” type with one switching point.

Słowa kluczowe

EN

optimal chemotherapy; Gompertzian growth

PL

chemioterapia

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Acta of Bioengineering and Biomechanics
• Rocznik: 2008
• Tom: Vol. 10, nr 2
• Strony: 81--84
• Opis fizyczny: Bibliogr. 9 poz., tab., wykr.

Twórcy

autor

Maroński R.

• Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics, ul. Nowowiejska 24, 00-665 Warsaw,,

Bibliografia

• [1] FORYŚ U., Matematyka w biologii, WN-T, Warszawa, 2005.
• [2] MAROŃSKI R., Metody rachunku wariacyjnego w biomechanice, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa, 1999.
• [3] MAROŃSKI R., “Strange” solutions of optimal control problem in cancer chemotherapy, Acta of Bioengineering and Biomechanics, 2004, Vol. 6, Suppl. 1, 105–109.
• [4] MAROŃSKI R., Optimal strategy in cancer chemotherapy for exponential model of cell population growth, Zeszyty Naukowe Katedry Mechaniki Stosowanej Politechniki Śląskiej, 2006, 26, 231–234.
• [5] MAROŃSKI R., Co ma wspólnego chemioterapia raka z mechaniką? Pierwszy Kongres Mechaniki Polskiej, Warszawa, 28–31 sierpnia 2007 (na płycie CD).
• [6] MIELE A., Extremization of linear integrals by Green’s theorem, [in:] Leitmann G. (ed.), Optimization techniques with application to aerospace systems, Academic Press, New York, London, 1962, 69–98.
• [7] NORTON L., A Gompertzian model of human breast cancer growth, Cancer Research, 1988, 48, 7067–7071.
• [8] ŚWIERNIAK A., DUDA Z., Some control problems related to optimal chemotherapy – singular solutions, Applied Mathematics and Computer Sciences, 1992, Vol. 2, No. 2, 293–302.
• [9] ŚWIERNIAK A., POLAŃSKI A., KIMMEL M., Optimal control problems arising in cell-cycle-specific cancer chemotherapy, Cell Prolif., 1996, 29, 117–139.