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2 Journal of Medical Informatics & Technologies

2 2004

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Finite dimensional models of drug resistant and phase specific cancer chemotherapy

Ledzewicz U., Schättler H., Świerniak A.

Journal of Medical Informatics & Technologies

2004

Vol. 8

IP5--14

The problem of modelling drug resistance and phase specificity of cancer chemotherapy using finite dimensional models were considered. We formulate optimal control problems arising in protocol design for such models and discuss research issues resulting from these formulations.

Are infinite dimensional models applicable in modelling and analysis of cancer chemotherapy?

Świerniak A., Kimmel M., Śmieja J., Rzeszowska-Wolny J.

Journal of Medical Informatics & Technologies

2004

Vol. 8

MM3--10

Drug resistance and phase dependence have been regarded by many authors as the main obstacles against successful cancer chemotherapy. We propose a model which takes into account both these phenomena and give a tool to use phase specificity as an advantage rather than a fault and make it resistant of drug resistance. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy, in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which enables decomposition of the model into two interacting subsystems. While the first one, of finite dimension, can have any form, the second one is infinite dimensional and tridiagonal.