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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.

Modelling of cell aging - system theoretic approach

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

Journal of Medical Informatics & Technologies

2001

Vol. 2, Part. 1

MI3--MI8

We characterize the asymptotic behavior of telomeres shortening of which is supposed to be the mechanism of aging and death. The problem is described by models in the form of infinitely many differential linear first order equations, resulting from branching random walk processes used to represent the evolution of particles in this problem, under different assumptions dealing with stochastic characterization of the process. We use control theoretical machinery based on Laplace transforms, Tauberian theorems and transfer loop reduction.